. (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 n & Z, n is odd if and only if n + 2 is odd.

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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 n € 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 n € 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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