Trigonometric substitution

Understand the problem Let with . Prove thatDetermine when equality holds. Source of the problem Singapore Team Selection Test 2004 Topic Inequalities Difficulty Level Medium Suggested Book Inequalities by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint 3Hint...

The non-existence of a polynomial

Understand the problem If is a polynomial with integer coefficients and , , , three distinct integers, then show that it is impossible to have , , . Source of the problem Indian National Mathematical Olympiad 1986 Topic Algebra Difficulty Level Easy Suggested Book An...

A linear functional equation

Understand the problem Find all functions such that for all Source of the problem Singapore Team Selection Test 2008 Topic Functional Equations Difficulty Level Medium Suggested Book Functional Equations by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint...
Lottery tickets

Lottery tickets

Understand the problem Each lottery ticket has a 9-digit number, which uses only the digits 1, 2, 3. Each ticket is coloured red, blue or green. If two tickets have numbers which differ in all nine places, then the tickets have different colours. Ticket 122222222 is...

Solve for n and k

Understand the problem Find all pairs of positive integers so that . Source of the problem Singapore MO 2008 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you really need a...