Unformatted text preview: 2 n + 1, with n ≥ 1. Note that p ≡ 1 mod 4. With this assumption, show that 7 ( p1) / 2 ≡ 1 mod p 3. a) ( 2 pts ) Let p be an odd prime, with p 6 = 5. Show that ±5 p ² = ±1 p ²± p 5 ² b) ( 4 pts ) Hence ﬁnd the congruence condition on an odd prime p 6 = 5, for which x 2 ≡ 5 mod p is solvable. 4. ( 2 pts ) Determine whether x 2 ≡ 35 mod 1003 is solvable (given that 1003 is a prime). 1...
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This note was uploaded on 06/15/2009 for the course MATH 115 taught by Professor Mok during the Fall '07 term at Berkeley.
 Fall '07
 MOK
 Number Theory, Congruence

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