Theorem 4.12. Gauss: Let n ‡0 (mod p). Consider the remainders mod p of the following(p-1)/2 many integers:P1n. 2n.2Let m be the number of these remainders which exceed p/2. Then (=) = (−1)™.-n.

Let n≢0mod p. Consider the remainders mod p of the following p-12 many integers, n, 2n,......,p-12n.…

Answered: Theorem 4.12. Gauss: Let n #0 (mod p).…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Theorem 4.12. Gauss: Let n #0 (mod p). Consider the remainders mod p of the following (p-1)/2 many integers: p-1 n. 2n. 2 Let m be the number of these remainders which exceed p/2. Then (=) = = (-1)m. -n.