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[rancid beacon]

does anyone understand this proof? (x, n) is supposed to be notation for the highest common factor and k is o(x) but i dont get it at all

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[inner lynx]

(x, n) means gcd(x, n)

= hcf(x, n)

[thin sundial]

In long form the argument goes like this: suppose n | kx for some k. Then equivalently n/(x,n) | k, hence n/(x,n) is minimal, also since (x,n) | x, it follows that n | xn/(x,n), hence the order of x is n/(x,n), as required.

@rancid beacon

[rancid beacon]

how do you go from n | kx to n/(x, n) | k

[thin sundial]

it's this part here