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Let m be the number of these remainders which exceed p/2. Then ( #) = (-1)m.

Let m be the number of these remainders which exceed p/2. Then ( #) = (-1)m.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 52E
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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 2 Let m be the number of these remainders which exceed p/2. Then (;) = (−1)™. n. 2n. .. -72.
Transcribed Image Text:Theorem 4.12. Gauss: Let n #0 (mod p). Consider the remainders mod p of the following (p-1)/2 many integers: P-1 2 Let m be the number of these remainders which exceed p/2. Then (;) = (−1)™. n. 2n. .. -72.
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