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If m, n, and p are three consecutive integers, then one of them must be even. Let's say the even number is m. Since m is even, it is divisible by two, and so can be written as 2*k, where k is some integer.

This means that

m*n*p = 2*k*n*p.

Since we are multiplying the quantity k*n*p by 2, it must be divisible by two, and therefore must be even.

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Q: Can you prove If m n and p are three consectuive integers then mnp is even?
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