Hello, I guess these problems are not supposed to be very hard, but I am confused.
1. Let . Prove that if and only if there exists such that .
2. Prove that if with and , then .
Thanks in advance.
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Let be a prime divisor of . Since has to divise or (because is irreducible).
But doesn't divide Hence and that is true for any prime divisor of
Therefore (Be more precise than me to show that )
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