Assume n and m are integers. Prove if m divides n, then m divides - n

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Mathematics

Mendoza

13 February, 18:29

Assume n and m are integers. Prove if m divides n, then m divides - n

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Huerta · Answer 1

Answer: So, if m divides n then n/m = x, and x is integer.

then - n/m = (-1*n) / m = - 1*n/m = - 1*x = - x.

So if x is integer, - x also is integer, then - n/m is integer and then m divides - n.

Where you used that in the integers set each number a has a opposite (also in the set) such that a + b = 0, and b = - a = - 1*a.