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] ???
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] ???