by Sankhadip Chakraborty

Understand the problem Given and for all , show that Source of the problem Singapore Mathematical Olympiad 2010 Topic Inequalities Difficulty Level Easy Suggested Book Inequalities by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you really... by Sankhadip Chakraborty

Understand the problem Determine all pairs of positive integers for which is a perfect square. Source of the problem Indian National Mathematical Olympiad 1992 Topic Number Theory Difficulty Level Easy Suggested Book An Excursion in Mathematics Start with hints Hint... by Sankhadip Chakraborty

Understand the problem a) Given any positive integer , show that there exist distint positive integers and such that divides for ; b) If for some positive integers and , divides for all positive integers , prove that . Source of the problem Indian National... by Sankhadip Chakraborty

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... by Sankhadip Chakraborty

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... by Sankhadip Chakraborty

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...