Mathematical Reflections – Archives

2026 Issues

Mathematical Reflections - Issue 5 2026
Article #1

Three Useful Lemmas in Solving Certain Inequalities of 4 Variables
by Titu Andreescu and Marius Stanean

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Article #2

Isogonal Conjugacy Without Angles: Generalizations and Properties of Remarkable Cevian Points
by Eldar Ussenov

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Problem Column

The deadline for submissions is November 15, 2026

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Solutions

Solutions to Mathematical Reflections 4, 2026:

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Mathematical Reflections – Issue 4 2026
Article #1

Deriving Th´ebault’s Configuration Properties and Sangaku Equal Circles through Geometry of Conic Sections
by Hussein Khayou

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Article #2

On Best Constants in Two Refinements of the Garfunkel–Bankoff Inequality
by Tran Quang Hung and Vuong Khanh Toan

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Problem Column

The deadline for submissions is September 15, 2026

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Solutions

Solutions to Mathematical Reflections 3, 2026:

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Mathematical Reflections – Issue 3 2026
Article #1

Quadratic Reciprocity, Thue’s Lemma, and Primes of the Form x2 + ny2
by Alikhan Serik

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Article #2

Applications of the Fundamental Symmetric Sums in the Study of Some Algebraic Inequalities
by Marius Dragan and Ovidiu T. Pop

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Problem Column

The deadline for submissions is July 15, 2026

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Solutions

Solutions to Mathematical Reflections 2, 2026:

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Mathematical Reflections – Issue 2 2026
Article #1

The (2k + 1)–Sector Problem in Right-Angled Triangles
by Andrei Eugeniu Patularu

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Article #2

On the Representation of Natural Numbers as Sums of Four Squares
by Titu Andreescu and Marian Tetiva

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Problem Column

The deadline for submissions is May 15, 2026

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Solutions

Solutions to Mathematical Reflections 1, 2026:

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Mathematical Reflections – Issue 1 2026
Article #1

On the Representation of the Natural Numbers as Sums of Two Squares
by Titu Andreescu and Marian Tetiva

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Article #2

Hidden Connections Between Wonderful Elements In The Geometry Of A Triangle – Part 2: Why Points
by Misha Nyzhnyk

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Problem Column

The deadline for submissions is March 15, 2026

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Solutions

Solutions to Mathematical Reflections 6, 2025:

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2025 Issues

Mathematical Reflections – Issue 6 2025
Article #1

Triples of Sums of Two Squares
by Titu Andreescu and Marian Tetiva

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Article #2

A Proof of Chebyshev’s Sum Inequality
by Adolf Cusmariu

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Problem Column

The deadline for submissions is January 15, 2026

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Solutions

Solutions to Mathematical Reflections 5, 2025:

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Mathematical Reflections – Issue 5 2025
Article #1

Intersecting Ideas: On Two Specific Points
by Shourya Sinha

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Article #2

The Best Constant in Some Inequalities – An Elementary Approach
by Neculai Stanciu and Titu Zvonaru

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Problem Column

The deadline for submissions is November 15, 2025

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Solutions

Solutions to Mathematical Reflections 4, 2025:

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Mathematical Reflections – Issue 4 2025

In Memory of Titu Zvonaru

A valuable contributor to Mathematical Reflections

  • Authored numerous mathematical articles, distinguished by their clarity of thought and expression, and conveyed the joy inspired by the beauty of mathematics.
  • Collaborated with many mathematicians, with a special interest in topics such as mathematical recreations, number theory, synthetic geometry, and inequalities.
  • Captivated others with the simplicity and clarity of his solutions.
  • Generous with his support to others, and succeeded in passing on his passion for mathematics to future generations through elegant problems and insightful articles.
  • View Titu’s Math Reflections contributions
Article #1

An Analytic Geometry Approach to Solving Certain Plane Geometry Problems
by Tran Quang Hung and Vuong Khanh Toan

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Article #2

On Huygens’s Trigonometric Inequality and Some Related Results
by Kiran Chandra Das

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Problem Column

The deadline for submissions is September 15, 2025

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Solutions

Solutions to Mathematical Reflections 3, 2025:

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Mathematical Reflections – Issue 3 2025
Article #1

On Prime Numbers of the Form a2 + ab + b2, Where a ∈ N+, b ∈ N+
by Arno Mikaelyan, Nairi Sedrakyan, Hayk Sedrakyan

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Article #2


by

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Problem Column

The deadline for submissions is July 15, 2025

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Solutions

Solutions to Mathematical Reflections 2, 2025:

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Mathematical Reflections – Issue 2 2025
Article #1

Zsigmondy’s Theorem and its Applications
by Sunaina Pati

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Article #2


by

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Problem Column

The deadline for submissions is May 15, 2025

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Solutions

Solutions to Mathematical Reflections 1, 2025:

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Mathematical Reflections – Issue 1 2025
Article #1

Hidden Connections Between Wonderful Elements in the Geometry of a Triangle
by Misha Nyzhnyk

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Article #2

by

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Problem Column

The deadline for submissions is March 15, 2025

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Solutions

Solutions to Mathematical Reflections 6, 2024:

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2024 Issues

Mathematical Reflections – Issue 6 2024
Article #1

The Trapezoid Law, Theorem and Their Applications
by Hayk Sedrakyan, Arno Mikaelyan, and Advik K.

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Article #2


by

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Problem Column

The deadline for submissions is January 15, 2025

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Solutions

Solutions to Mathematical Reflections 5, 2024:

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Mathematical Reflections – Issue 5 2024
Article #1

Generalization of Napoleon’s Theorem: Similar Triangles
by Jiri Blazek and Pavel Pech

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Article #2

by

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Problem Column

The deadline for submissions is November 15, 2024

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Solutions

Solutions to Mathematical Reflections 4, 2024:

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Mathematical Reflections – Issue 4 2024
Article #1

Some Generalizations of a Geometric Problem from USA TSTST
by Tran Quang Hung and Nguyen Cung Thanh

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Article #2


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Problem Column

The deadline for submissions is September 15, 2024

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Solutions

Solutions to Mathematical Reflections 3, 2024:

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Mathematical Reflections – Issue 3 2024
Article #1

Four Circles Tangent to an Ellipse
by Waldemar Pompe

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Article #2


by

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Problem Column

The deadline for submissions is July 15, 2024

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Solutions

Solutions to Mathematical Reflections 2, 2024:

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Mathematical Reflections – Issue 2 2024
Article #1

On the Calculation of a Series Involving the Product of the Tail and Harmonic Numbers
by Vincent Nguyen

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Article #2


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Problem Column

The deadline for submissions is May 15, 2024

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Solutions

Solutions to Mathematical Reflections 1, 2024:

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Mathematical Reflections – Issue 1 2024
Article #1

An Asymptotic Analysis on the Distribution of Primes via a Continuous Extension of the Factorial Function
by Srijan Sundar

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Article #2


by

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Problem Column

The deadline for submissions is March 15, 2024

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Solutions

Solutions to Mathematical Reflections 6, 2023:

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2023 Issues

Mathematical Reflections – Issue 6 2023
Article #1

Distance Formula for a Point Inside a Triangle
by Hayk Sedrakyan and Diya Gandhi

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Article #2

The Best Constant for an Inequality from Mathematical Reflections
by Titu Andreescu and Marius Stanean

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Problem Column

The deadline for submissions is January 15, 2024

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Solutions

Solutions to Mathematical Reflections 5, 2023:

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Mathematical Reflections – Issue 5 2023
Article #1

Chasing a Red Herring
by Titu Andreescu and Marian Tetiva

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Article #2

A New Method to Solve and Refine Algebraic Inequalities
by Mihaly Bencze and Marius Dragan

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Problem Column

The deadline for submissions is November 15, 2023

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Solutions

Solutions to Mathematical Reflections 4, 2023:

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Additional Resources
Coming Soon!
Mathematical Reflections – Issue 4 2023
Article #1

On a Class of Functional Equations
by Titu Andreescu and Marian Tetiva

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Article #2

Projective plane, Extended Complex Plane
by Nguyễn Minh Hà

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Problem Column

The deadline for submissions is September 15, 2023

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Solutions

Solutions to Mathematical Reflections 3, 2023:

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Mathematical Reflections – Issue 3 2023
Article #1

A Triangle Ratio Theorem and its Generalization to Higher Dimensions
by Hari Rajesh

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Article #2

Newton’s Quadrilateral Theorem
by Waldemar Pompe

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Problem Column

The deadline for submissions is July 15, 2023

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Solutions

Solutions to Mathematical Reflections 2, 2023:

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Mathematical Reflections – Issue 2 2023
Article #1

On a Combinatorial Identity
by Virgil Domocos

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Article #2


by

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Problem Column

The deadline for submissions is May 15, 2023

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Solutions

Solutions to Mathematical Reflections 1, 2023:

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Mathematical Reflections – Issue 1 2023
Article #1

A Few Generalizations of the Euler’s Totient Function
by Suzy Manuela Prajea

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Article #2

Solutions for the Frobenius Number in Three Variables
by Srijan Sundar

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Problem Column

The deadline for submissions is March 15, 2023

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Solutions

Solutions to Mathematical Reflections 6, 2022:

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2022 Issues

Mathematical Reflections – Issue 6 2022
Article #1

An Interesting Generator of Parabolic Systems of Coaxial Circles Using Apollonius’ Problem
by Tran Quang Hung and Truong Tuan Nghia

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Article #2

by

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Problem Column

The deadline for submissions is January 15, 2023

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Solutions

Solutions to Mathematical Reflections 5, 2022:

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Additional Resources
This is a must have book for the MR readers
Mathematical Reflections – Issue 5 2022
Article #1

Sperner’s Lemma and Brouwer’s Fixed Point
by Farzad Rashidi

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Article #2


by

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Problem Column

The deadline for submissions is November 15, 2022

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Solutions

Solutions to Mathematical Reflections 4, 2022:

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Additional Resources
This is a great book for the MR readers
Mathematical Reflections – Issue 4 2022
Article #1

Local Monotony and Continuity
by Suzy Manuela Prajea

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Article #2

Formulas for Diagonals of any Quadrilateral
by Hayk Sedrakyan, Aidan Mozayeni

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Problem Column

The deadline for submissions is September 15, 2022

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Solutions

Solutions to Mathematical Reflections 3, 2022:

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Additional Resources
Any student interested in mathematics would cherish and enjoy this unique collection of meaningful problems and solutions.
Mathematical Reflections – Issue 3 2022
Article #1

The Missing Dominant Terms in a Fourier Series
by C. S. Jog

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Article #2

Solving Functional Equations in R+ Using Inequalities and Sequences
by Mohammad Hossein Rezaei

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Problem Column

The deadline for submissions is July 15, 2022

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Solutions

Solutions to Mathematical Reflections 2, 2022:

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Additional Resources
Any student interested in mathematics would cherish and enjoy this unique collection of meaningful problems and solutions.
Mathematical Reflections – Issue 2 2022
Article #1

Three Reflections
by Waldemar Pompe

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Article #2

A New Approach to the Interior Goat and Bird Problems
by C. S. Jog

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Problem Column

The deadline for submissions is May 15, 2022

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Solutions

Solutions to Mathematical Reflections 1, 2022:

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Additional Resources
Two new books are great resources for students who need to practice for the summer program admission test or for math enthusiasts to work on their problem solving skills.
Mathematical Reflections – Issue 1 2022
Article #1

Concurrency, Coliniarity, and Cyclicity using Homotheties
by Dr. Suzy Manuela Prajea

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Article #2

More on an Extension of Fagnano’s Problem
by Nguyen Minh Ha

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Problem Column

The deadline for submissions is March 15, 2022

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Solutions

Solutions to Mathematical Reflections 6, 2021:

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Additional Resources
Two new books are great resources for students who need to practice for the summer program admission test or for math enthusiasts to work on their problem solving skills.