If $a$ is a positive integer of the type $3n+2$,then pove that at-least one prime divisor of $a$ is of the form $3n+2$
My try:If $3n+2$ is prime then we are done since $3n+2$ is of the form $3n+2$. What do we do in the case it isn't prime?
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3Hint: What happens if you multiple two primes which are equivalent to $1\pmod 3$? – Michael Burr Mar 30 '17 at 11:19
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Trivial question: if every prime divisor of $3n+2$ were of the form $3k+1$ then $3n+2$ would be of the same form, contradiction. It follows that every number of the form $3n+2$ has to have a prime divisor of such a form. – Jack D'Aurizio Mar 30 '17 at 13:23