Prime numbers

If p is prime ,and x is prime to p,show that xpr-pr-1-1 is divisible by pr

2 Answers

11
Devil ·

Obvious for r=1, so let r=2+b, where b≥0
From Fermat's Little Theorem, we have
xp-1≡1(modp), where p is a prime....
Raise both sides to the power p1+b
The result follows.

1
champ ·

Oh yes .
it was easy :P

thank you anyways :-)

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