Originally Posted by

**integral** I'm trying really hard to get good at making proofs. It is extremely hard for me, much more so than anything else I have ever done. I've tried to prove the title above but I don't know if my proof is logical.

lemma: "If n > 1 then there is a prime p such that p | n ."

n and k are integers.

proof:

Assume that there is no such p for n>1 such that $\displaystyle \frac{n}{p}=k$

This would imply that $\displaystyle pk\neq n$ for any prime value of p.

This also implies that there are no primes that can be expressed as the division of two integers. $\displaystyle p\neq \frac{n}{k}.$

However if this was true, prime numbers would be irrational which they are not.

Therefore all numbers>1 are divisable by a prime?

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I'm not sure if this is logical. If it is not please don't post the proof, just give me a hint?