Linear recurrences

Linear difference equations Definition A linear difference equation is a recurrence relation of the form . If , then it is called homogeneous. In this article, we shall also assume for convenience. The name “difference equation” is a nod to the fact that...

An inductive inequality

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...

A search for perfect squares

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...

INMO 1996 Problem 1

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...