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[tex]f(x)[/tex] will give us the smallest integer [tex]m[/tex] such that [tex]y^m \equiv 1 \bmod{x}[/tex] 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 text alone.

I'm guessing that the Chinese remainder theorem is applicable here.

Also if we let p be prime then I know that f(p) will give the result of (p-1). This is basically proved with Euler's theorem.

Is this true or is Euler's theorem not so easily applicable here? I guess the fact that here m is the smallest integer, where's in Euler's it's not the smallest, but it's easy to prove that this doesn't matter using groups.

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 text alone.

I'm guessing that the Chinese remainder theorem is applicable here.

Also if we let p be prime then I know that f(p) will give the result of (p-1). This is basically proved with Euler's theorem.

Is this true or is Euler's theorem not so easily applicable here? I guess the fact that here m is the smallest integer, where's in Euler's it's not the smallest, but it's easy to prove that this doesn't matter using groups.

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