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(a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n € Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.

(a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n € Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is 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
Problem 1RQ
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7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n e Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.
Transcribed Image Text:7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n e Z, n³ +n is even. (c) Prove that for all ne Z, n is odd if and only if n + 2 is odd. (d) Prove that the product of two consecutive integers is even.
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