Fermat's little theorem

YM30

New member
Joined
Oct 12, 2018
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2
Hi, I'd like some help for the following problem :
p is a prime number (odd number)
a,b whole numbers
p l (a2 + b2)
p does not divide a

I have proven that there is c such as ac ≡ 1 [p]
and x such as x2
≡ -1[p]
How can I prove that p
≡ 1[4] with Fermat's little theorem ?

We know that we have either p
≡ 3[4] or p≡ 1[4].
ap-1
≡ 1[p]
ap-1-1
≡ 0[p]
(a(p-1)/2-1)
(a(p-1)/2+1)≡ 0[p] ??? :(:(
 
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