Unformatted text preview: p ). Write p1 = qs + r for some q,r âˆˆ Z with 0 â‰¤ r < s . (a) Starting with a p1 â‰¡ 1 (mod p ), prove that a r â‰¡ 1 (mod p ). (b) Explain why r must equal 0. (c) Explain why s  ( p1). (d) Find the smallest positive integer s for which 8 s â‰¡ 1 (mod 23). Problem 3 . (a) Find 41 515 (mod 17). (c) Find 100 âˆ‘ k =1 k k ! (mod 11). Problem 4 . In Z 20 , solve the pair of simultaneous equations [3][ x ] + [5][ y ] = [6] [5][ x ] + [7][ y ] = [14] 1...
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This note was uploaded on 12/10/2010 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS
 Math

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