Show that if n is an integer and n^3 + 5 is odd then n is even

Question

Mathematics

Madeline Snow

27 February, 22:02

Show that if n is an integer and n^3 + 5 is odd then n is even

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Answers (1)

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Edith Cooley · Answer 1

If n is odd then its cube is also odd because odd times odd is odd. When we add 5, an odd number, we get an even number.

If n is even, its cube is also even so adding an odd number makes the sum odd. So if the expression is odd, n must be even.