Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
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1.4.3 Extracting Square Roots modulo p<br />
Theorem 1.6 For prime numbers p ≡ 3(mod4)and a ∈ QR p ,wehave<br />
that r = a (p+1)/4 mod p is a square root of a.<br />
Proof.<br />
(a (p+1)/4) ) 2 ≡ a (p−1)/2 · a (mod p)<br />
≡ a (mod p)(Fermat, sec. 1.3)