MathDB

43

Part of 1992 IMO Longlists

Problems(1)

Find all positive integers n with φ(n) | n and a condition

Source:

9/2/2010
Find the number of positive integers nn satisfying ϕ(n)∣n\phi(n) | n such that ∑m=1∞([nm]−[n−1m])=1992\sum_{m=1}^{\infty} \left( \left[ \frac nm \right] - \left[\frac{n-1}{m} \right] \right) = 1992 What is the largest number among them? As usual, ϕ(n)\phi(n) is the number of positive integers less than or equal to nn and relatively prime to n.n.
floor functionnumber theoryrelatively primeseries summationNumber theoretic functionsIMO ShortlistIMO Longlist