# Problem 9 of Finnish matriculation exam spring 2017 Mathematics (advanced level)

Assuming that $$p, q$$ and $$r$$ are positive integers, show that
$(p+q)(q+r)(r+p)$ is even.

Note by Jesse Nieminen
1 year, 6 months ago

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If at least two out of the three numbers are even or odd(since their sum will be even), the question is proved. But in any three numbers, at least two numbers will be either even or odd.

- 1 year, 6 months ago

Yep.

- 1 year, 6 months ago