5) Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4. In other words, prove that it is not 4 4 ' = 4 k+3, for integers n, m and k. [Hint: possible for n +m Consider fourth powers of even and odd integers.]

Q: Prove for any positive integer n, n=floor(n/2) + ceiling(n/2)

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Q: 7. Prove that 4 3m² – n² for all odd integers m and n.

A:

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Q: 32. Prove that 3 divides n³ +2n whenever n is a positive integer.

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A: Ans : page 1:Ans page 2:

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer