(a) Prove that any integer = a (mod m) is divisible by (a,m). (b) Deduce that...

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(a) Prove that any integer = a (mod m) is divisible by (a,m). (b) Deduce that if (a, m) > 1 and if there is a prime = a (mod m), then that prime is (a,m). (c) Give examples of arithmetic progressions which contain exactly one prime and examples which contain none. (d) Show that the arithmetic progression 2 (mod 6) contains infinitely many prime powers. (a) Prove that any integer = a (mod m) is divisible by (a,m). (b) Deduce that if (a, m) > 1 and if there is a prime = a (mod m), then that prime is (a,m). (c) Give examples of arithmetic progressions which contain exactly one prime and examples which contain none. (d) Show that the arithmetic progression 2 (mod 6) contains infinitely many prime powers.

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a Let n be an integer such that n a mod m then there exists an integer k such that n a km Now let d ... View the full answer