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Problems(1)

φ(n,m) a new function for every n

Source:

9/1/2010
Let ϕ(n,m),m≠1\phi(n,m), m \neq 1, be the number of positive integers less than or equal to nn that are coprime with m.m. Clearly, ϕ(m,m)=ϕ(m)\phi(m,m) = \phi(m), where ϕ(m)\phi(m) is Euler’s phi function. Find all integers mm that satisfy the following inequality: ϕ(n,m)n≥ϕ(m)m\frac{\phi(n,m)}{n} \geq \frac{\phi(m)}{m} for every positive integer n.n.
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