PS: Please answer all the subparts correctly as they are both connect in the same questions in word processing not handwritten on JPEG Format.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: (b) Prove that for every n e Z, n³ +n…

(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.

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

PS: Please answer all the subparts correctly as they are both connect in the same questions in word processing not handwritten on JPEG Format.

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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