math362assignment2.pdf - Math 362 Assignment 2 Due...

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Math 362 Assignment 2Due: Wednesday, October 4Answer all questions. Each question is worth 5 marks. Full marks will be awarded onlyfor answers that are both mathematically correct and coherently written.1.(a) Given thatk°2 (mod 7), determine the least residue of5k2+ (17)3(mod 7).(b) Given thatk°5 (mod 8), determine the least residue of3k333+ 19 (mod 8).Answer
2. Use congruences to prove that(a) ifn >2is prime, thenn°1or3 (mod 4),(b) ifn >3is prime, thenn°1or5 (mod 6),(c) ifn°3 (mod 4), thenncannot be written as the sum of the squares of twointegers (Remember this result!).Answer
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