MATH1823 Midterm: MATH 1823 UNB Exam 1823 99d
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Math 250 take-home final exam due monday, may 7 at noon. Please note that the exam contains six questions listed on two pages which are worth a total of 100 points: (20 points) (see silverman, pp. Let a, b z, and suppose that b is an odd positive integer. Write b = p1p2 pn as a product of (not necessarily distinct) odd primes. De ne the jacobi symbol (cid:16) a the following product of legendre symbols: b(cid:17) to be b(cid:17) = (cid:18) a (cid:16) a p1(cid:19)(cid:18) a b(cid:19) = (cid:26) +1, if b 1 or 7 (mod 8), 1, if b 3 or 5 (mod 8). p2(cid:19) (cid:18) a pn(cid:19) . (a) prove (cid:18)2 (b) assume a is odd and positive. Prove(cid:16) a b(cid:17) = (cid:18) b a(cid:19), if a 1 (mod 4) or b 1 (mod 4), a(cid:19), if a b 3 (mod 4). (cid:18) b: (15 points) (see silverman, exercise 25. 5, p.
