MAD 4301 Midterm: MAS4301 C97 Test 1
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Instructions: do not write your answers on this paper, use separate answer sheets. If ax + by = 1, then (a, b) = 1. (6) (16 points) prove: If (a, m) = 1, then ax 1 (mod m) for some integer x. (7) (16 points) we proved the following lemma. If p is a prime number and p|ab, then p|a, or p|b. Using this lemma and mathematical induction, prove: if p is a prime num- ber, n 1 and p divides a product then p divides one of the factors aj. a1a2 . an ,
