If xy ≡ 1 (modulo n) st x, y, n are natural numbers, then x, y have the same order modulo n.

I tried direct proof and contradiction, but was stuck both ways.

I really need help on dis, thank u.

-Frank

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- Apr 19th 2009, 07:00 PMFrankTheTankOrder modulo proof help
If xy ≡ 1 (modulo n) st x, y, n are natural numbers, then x, y have the same order modulo n.

I tried direct proof and contradiction, but was stuck both ways.

I really need help on dis, thank u.

-Frank - Apr 21st 2009, 02:06 AMclic-clac
Hi

Quote:

If xy ≡ 1 (modulo n) st x, y, n are natural numbers, then x, y have the same order modulo n.

Let be the order of i.e. and for any

What about ? Let be a positive divisor of what can you say about ? Conclusion?