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4. Let a, b = Z, and let p be a prime. If p does not divide ab, then p does not divide a and p does not divide b. 5. There exists no integers j, k for which 18j + 6k = 1. 6. Suppose m, n € Z. Prove that if 4 divides m² + n², then m and n are both even.

4. Let a, b = Z, and let p be a prime. If p does not divide ab, then p does not divide a and p does not divide b. 5. There exists no integers j, k for which 18j + 6k = 1. 6. Suppose m, n € Z. Prove that if 4 divides m² + n², then m and n are both even.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. Let a, b € Z, and let p be a prime. If p does not divide ab, then p does not divide a and p does not divide b. 5. There exists no integers j, k for which 18j + 6k = 1. 6. Suppose m, n € Z. Prove that if 4 divides m² + n², then m and n are both even.
Transcribed Image Text:4. Let a, b € Z, and let p be a prime. If p does not divide ab, then p does not divide a and p does not divide b. 5. There exists no integers j, k for which 18j + 6k = 1. 6. Suppose m, n € Z. Prove that if 4 divides m² + n², then m and n are both even.
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