Question

4. Show that if n is any integer, then n^2 3n 5 is an odd integer

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Frederik

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68 Answers

Suppose the n is odd
If n is odd, then n^2 will be odd
If n is odd, then 3n will be odd
We know that 5 is odd
So,
odd + odd + odd = odd
Suppose the n is even
If n is even, then n^2 will be even
If n is even, then 3n will be even
We know that 5 is odd
So,
even + even + odd = odd
Hence n^2 + 3n + 5 is always odd

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