extra-homework2

extra-homework2 - the coe cient of the hishest power of t )...

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Extra Exercises for 1/26 1. Show that if p is an odd prime and a 2 Z is such that p - a and k 1 then a p k 1 ( p 1) ± 1 mod p k : 2. Prove under the hyptheses in 1. that a p k 1 ( p 1) ² 1 p k ± a p 1 ² 1 p mod p: 3. Let = e 2 3 : Find f ( t ) = a 0 + a 1 t + a 2 t 2 + t 3 with a i 2 Z for i = 0 ; 1 ; 2 ; 3 such that f (1 + ) = 0 : Is there another monic (coe¢ cient of
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Unformatted text preview: the coe cient of the hishest power of t ) polynomial of degree at most 3 with integer coe cients, g ( t ) , such that g (1 + & ) = 0? 1...
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