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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.

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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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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