7. Nontrivial square roots of 1 (a) Count the number of n between 1 and 1000 such...

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7. Nontrivial square roots of 1

(a) Count the number of n between 1 and 1000 such that there are exactly 14 non-

trivial square roots of 1 modulo n (the trivial ones are 1 and n − 1).

(b) Repeat part

(a) with 4 in place of 14. How many n do you count now?

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