Understand the problem Let be positive real numbers such that . Prove that Source of the problem Singapore Team Selection Test 2008 Topic Inequalities Difficulty Level Medium Suggested Book Inequalities by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint 3Hint...

Understand the problem Find all non-zero real numbers which satisfy the system of equations: Source of the problem Indian National Mathematical Olympiad 2010 Topic Algebra Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint...

Understand the problem Z be the set of all integers. Determine all f : Z -> Z such that, for all integers a, b Source of the problem IMO 2019 Problem 1 Topic Functional Equation Difficulty Level 5 out of 10 Suggested Book Functional Equation and How to Solve...

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...

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...

Understand the problem Positive integers and are each less than . What is the smallest possible value for ? Source of the problem 2013 AMC 10B Problem 5 Topic Inequality Difficulty Level 3 out of 10 Suggested Book Inequalities: A Mathematical Olympiad Approach Start...