Number Theory – Croatia MO 2005 Problem 11.1

Number Theory – Croatia MO 2005 Problem 11.1

Understand the problem Find all positive integer solutions of the equation  Source of the problem Croatia MO 2005 Topic Number Theory Difficulty Level 6/10 Suggested Book Challenges and Thrills in Pre College Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4...
SMO(senior)-2014 Problem 2 Number Theory

SMO(senior)-2014 Problem 2 Number Theory

Understand the problem Find, with justification, all positive real numbers      satisfying the system of equations:     Source of the problem SMO (senior)-2014 stage 2 problem 2 Topic Number Theory Difficulty Level Easy Suggested Book Excursion in Mathematics Start...
SMO (senior) -2014/problem-4 Number Theory

SMO (senior) -2014/problem-4 Number Theory

Understand the problem For each positive integer  let    where     are the first  primes. Prove that for each positive integer , there is an integer  such that    Source of the problem SMO (senior)-2014 stage 2 problem 4 Topic Number Theory Difficulty Level Medium...
The best exponent for an inequality

The best exponent for an inequality

Understand the problem Let  be positive real numbers such that .Find with proof that  is the minimal value for which the following inequality holds: Source of the problem Albania IMO TST 2013 Topic Inequalities Difficulty Level Medium Suggested Book Inequalities by BJ...
A functional inequation

A functional inequation

Understand the problem Find all functions  such thatholds for all . Source of the problem Benelux MO 2013 Topic Functional Equations Difficulty Level Easy Suggested Book Functional Equations by BJ Venkatachala Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you...