# Cheenta Reading Room

Outstanding problems, discussion and more## Brazil MO 2018 Problem 2 – Azambuja Rational

This problem is a beautiful application of Invariance principle and storng form of induction from brazil MO 2018.

read more## A sequence of polynomials and an invariant

Understand the problemDefine a sequence of functions by for . Prove that each is a polynomial with integer coefficients. Indian National Mathematical Olympiad 2012 Sequences Easy Problem Solving Strategies by Arthur Engel Start with hintsDo you really need a...

read more## Primes in arithmetic progression

Understand the problemSuppose that are prime numbers forming an arithmetic progression with common difference . If show that . Singapore Mathematical Olympiad 2010 Number Theory Easy Elementary Number Theory by David Burton Start with hintsDo you really need a...

read more## An inequality with many unknowns

Understand the problemLet be positive real numbers such that . Prove thatSingapore Team Selection Test 2008InequalitiesMediumInequalities by BJ VenkatachalaStart with hintsDo you really need a hint? Try it first!Use the method of contradiction.Suppose that $latex...

read more## Isomorphism in b/w infinite dim vector sp: TIFR GS 2019, Part B Problem 10

It is a question on isomomorphisms b/w inf dim vector spaces. It was asked in TIFR 2019 GS admission paper. It is a true false question.

read more## Matrix to real line: TIFR GS 2019, Part B Problem 8

It is a lie algebra question on connections b/w matrices and real space. It was asked in TIFR 2019 GS admission paper. It is a true false question.

read more## Homomorphism to Continuous function: TIFR GS 2019, Part B Problem 9

It is a lie algebra question on homomorphisms b/w real ring and ring of continuous function. It was asked in TIFR 2019 GS admission paper. It is a true false question.

read more## Similar matrices: TIFR GS 2019, Part B Problem 7

It is a linear algebra question on similar matrices. It was asked in TIFR 2019 GS admission paper. It is a true false question.

read more## Looks can be deceiving

Understand the problemFind all non-zero real numbers which satisfy the system of equations:Indian National Mathematical Olympiad 2010AlgebraMediumAn Excursion in MathematicsStart with hintsDo you really need a hint? Try it first!When a polynomial equation looks...

read more## IMO, 2019 Problem 1 – Cauchyish Functional Equation

This problem is a patient and intricate and simple application of Functional Equation with beautiful equations to be played aroun with.

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