Assume that the integer r is a primitive root of the prime p, where p = 1 (mod 8).(a)

Chapter 9, Problem 8

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Assume that the integer r is a primitive root of the prime p, where p = 1 (mod 8).(a) Show that the solutions of the quadratic congruence x2 = 2 (mod p) are given byx = (r ?(pl)/S + r(p-1)/S) (mod p)[Hint: First confirm that r3(pl)/2 = -1 (mod p).](b) Use part (a) to find all solutions to the two congruences x2 = 2 (mod 17) and x2 = 2(mod 41).

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