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Unformatted text preview: (i) gcd( a, b ) = gcd( x, y ) = 1; (ii) gcd( a, b ) = 17 and gcd( x, y ) = 1; (iii) gcd( a, b ) = 1 and gcd( x, y ) = 17; (iv) gcd( a, b ) = gcd( x, y ) = 17. 5 (6 points) . Suppose that n is composite: an integer greater than 1 that is not prime. Show that ( n-1)! and n are not relatively prime. Prove that the congruence ( n-1)! -1 mod n is false. 6 (6 points) . Prove that-1 is not a square modulo the prime p if p 3 mod 4. 7 (6 points) . Show that x 8 1 mod 20 if x is an integer that is prime to 20. Find the integer t such that t 9 = 760231058654565217 7 . 60231 10 17 ....
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- Spring '08