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.

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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...

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Question

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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