by Sankhadip Chakraborty

Understand the problem Define a sequence by , andfor For every and prove that divides. Suppose divides for some natural numbers and . Prove that divides Source of the problem Indian National Mathematical Olympiad 2010 Topic Number Theory Difficulty Level... by Sankhadip Chakraborty

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... 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...