Prove the following results. (I). If n = 2(mod 4), then n is the sum of three squares of integers. (II). If n = 1(mod 8), then n is the sum of three squares of integers. (III). If n = 3(mod 8), thenn is the sum of three squares of integers.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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Prove the following results.
(I). If n = 2(mod 4), then n is the sum of three squares of integers.
(II). If n = 1(mod 8), then n is the sum of three squares of integers.
(III). If n = 3(mod 8), then n is the sum of three squares of integers.
Transcribed Image Text:Prove the following results. (I). If n = 2(mod 4), then n is the sum of three squares of integers. (II). If n = 1(mod 8), then n is the sum of three squares of integers. (III). If n = 3(mod 8), then n is the sum of three squares of integers.
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