An example in my textbook, but I'm not quite sure how to set this one up, because of the $p \ge 5$ part. How do I start it off?
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Suppose that, for example, $p$ gives the remainder 2. What does it say you about number p? – Wojowu Oct 10 '14 at 20:02
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If $p\ge 5$, then $p$ is odd. So, the remainder has to be odd. But, the remainder cannot be $3$ because $p\ge 5$ cannot be the form $6m+3$ which is divisible by $3$.
mathlove
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Okay, and then how would I show that the remainder has to be odd? I can do examples and see that it is true, but how would I generally prove it? – JCMcRae Oct 10 '14 at 20:13
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1@J-Play: If the remainder is even $2m$, $p$ can be represented as $p=6k+2m$. This is even, which is a contradiction (a prime number $p\ge 5$ is odd). – mathlove Oct 10 '14 at 20:16