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I'm suppose to prove this but i'm having troubles figuring out how u find "distinct" integers. Meaning they can't be the same number. i figured it out they just wanted integers though. Here is the question:

There are distinct integers m and n such that 1/m + 1/n is an integer.

I wrote:

Let m = n = 1. Then m and n are integers such that 1/m + 1/n = 1/1 + 1/1 = 2, which is an integer.

Is there a processes to figuring these things out or is it a guessing game?

Also a harder one is this one:

There is an integer n such that 2n^2-5n+2 is prime.

I looked up what the defintion of a prime number is and i got the following:

An integer n is prime if and only if n > 1 and for all positive integers r and s, if n = (r)(s), then r = 1, or s = 1.

So i wasn't sure where to start with that so I tried to factor 2n^2+5n+2 to see what happens and i got: (x-2)(2x-1). x = 2 or x = 1/2. Because 1/2 is not greater than 1 (x = 1/2) does this mean the whole expression is also not prime? Is that enough to prove it? IT says there IS an integer n that makes that expression prime though.

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# Homework Help: Proving statements, having issues finding distinct integers and also prime question

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