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.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 4TFE: Label each of the following statements as either true or false. a is congruent to b modulo n if and...
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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)™.
-n.
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 n. 2n. 2 Let m be the number of these remainders which exceed p/2. Then (=) = (−1)™. -n.
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