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rn is not divisible by 3k +1 or n = 3k + 2.

rn is not divisible by 3k +1 or n = 3k + 2.

Advanced Engineering Mathematics
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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6. In this problem, you may use the fact (which we will prove in Chapter 6) that an integer n is not divisible by 3 if and only if there exists an integer k such that n = 3k +1 or n = 3k + 2. (a) Prove that for all integers n, if 3 | n2, then 3 | n. (b) Prove that for all integers i and j, if 3 | (i2 + j?), then 3 | i and 3 | j.
Transcribed Image Text:6. In this problem, you may use the fact (which we will prove in Chapter 6) that an integer n is not divisible by 3 if and only if there exists an integer k such that n = 3k +1 or n = 3k + 2. (a) Prove that for all integers n, if 3 | n2, then 3 | n. (b) Prove that for all integers i and j, if 3 | (i2 + j?), then 3 | i and 3 | j.
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