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f(x) will give us the smallest integer m such that y^m \equiv 1 \bmod{x} given that x and y are coprime how would one go about showing that this function is multiplicative? I'm trying to do some Number Theory self study, and the problems I'm encountering are quite difficult to figure out from...

So how would you go about proving for example that P[X>x] > f(x) if you're given some f(x)

Suppose X is the standard normal variable. is it possible to find P(X>x)? i.e does the function have a defined integral? How would you show that it is or is not defined? What information can we obtain about P(X>x).