Show that if 7 | x^2 + 1, then 13 | x^3 + 5x^2 +17x - 100. I'm really not sure how to do this other than use the definition of divisibility, though I don't know where to go after that.
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Originally Posted by Snooks02 Show that if 7 | x^2 + 1, then 13 | x^3 + 5x^2 +17x - 100. I'm really not sure how to do this other than use the definition of divisibility, though I don't know where to go after that. The statement is never satisfied for any integer. Therefore, the conditional that is immediately true.
Originally Posted by Snooks02 Show that if 7 | x^2 + 1, then 13 | x^3 + 5x^2 +17x - 100. I'm really not sure how to do this other than use the definition of divisibility, though I don't know where to go after that. Have you checked to see if this true? In particular, what is the smallest value of x such that 7 divides x^2+ 1?
If we had (1) we see immediately that and then, by Fermat's little Theorem (*): , however, (1) implies: which is a contradiction! In fact there exists such that ( p is a prime with ) if and only if
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