Show that if m p1 pr is a product of distinct odd primes t

Show that if m = p_1, .. .p_r is a product of distinct odd primes, the set of odd a such that (a/m) = 1 are those lying in half of the congruence classes b modulo m such that gcd(b, m) = 1. As a corollary, deduce that for any odd integer n > 1, which is a product of distinct primes, the primes p such that (n/p) = 1 are those in one of phi(n) congruence classes of the 2 phi (n) congruence classes modulo 4n which can contain odd numbers.

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 Show that if m = p_1, .. .p_r is a product of distinct odd primes, the set of odd a such that (a/m) = 1 are those lying in half of the congruence classes b mod

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