Unformatted text preview: k ) (0 ≤ k ≤ p + 1) are divisible by p ? [Example: The seven binomial coeﬃcients ( 6 k ) are 1, 6, 15, 20, 15, 6, 1; the middle three are divisible by 5.] 4 (7 points) . Let p be a prime and let n be a nonnegative integer. Suppose that a is an integer prime to p . Show that b := a p n satisﬁes b ≡ a mod p and b p1 ≡ 1 mod p n +1 . 5 (6 points) . Show that n 4 + n 2 + 1 is composite for all n ≥ 2....
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 Spring '08
 ISBER
 Number Theory, Natural number, Prime number, K. A. Ribet

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