. Let p be an odd prime number. Write the quantityas a fraction Ap/Bp in lowest terms.(a)...

. Let p be an odd prime number. Write the quantity

as a fraction Ap/Bp in lowest terms.

(a) Find the value of Ap (mod p) and prove that your answer is correct.

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(b) Make a conjecture for the value of Ap ( mod p2 ) .

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(c) Prove your conjecture in (b). (This is quite difficult.)