PS: Please complete all of the subparts as they are all the same question and not in Handwritten paper. 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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Answered: 7. (a) Prove that m³ + 2n² = 36 has no…

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.