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Unformatted text preview: a, · · · , ( p − 1) · a are congruent modulo p . (b) Conclude from part (a) that the product of 1 , 2 , · · · , p − 1 is congruent 1 modulo p to the product of a, 2 a, · · · , ( p − 1) a . Use this to show that ( p − 1)! ≡ a p-1 ( p − 1)! ( mod p ) (c) Use Wilson’s theorem to show that a p-1 ≡ 1 (mod p ) if a is not divisible by p . (d) Use part (c) to show that a p ≡ a (mod p ) for all integers a . Problem 7. Complete the proof of the Chinese Remainder Theorem by showing that the simultaneous solution of a system of linear congruences modulo pairwise relatively prime integers is unique modulo the product of these moduli. 2...
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This note was uploaded on 02/06/2011 for the course ECE 423 taught by Professor Dolatabadi during the Spring '11 term at Amirkabir University of Technology.
- Spring '11