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Outstanding problems, discussion and 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...

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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...

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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...

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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...

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