φ(n,m) a new function for every n
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September 1, 2010
functioninequalitiesnumber theoryrelatively primeNumber theoretic functionsIMO ShortlistIMO Longlist
Problem Statement
Let , be the number of positive integers less than or equal to that are coprime with Clearly, , where is Euler’s phi function. Find all integers that satisfy the following inequality:
for every positive integer