Square Roots in Number Theory

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Let N=pq, with p and q primes, with p congruent to 7 mod 8 and q congruent to 3 mod 8. We have seen in class that if h is relatively prime to N, then

h=efs, where e= 1 or -1, f= 1 or 2, and s=r^2 for some r.

Verify this fact when N=77 for each of the values of h from 1 to 6 and 8 to 10.

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This is wrong as stated: Take $p=7, q=3, h=5!$ Other counter-examples are all primes $h \ne p,q.$