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12 Nov 2019
Find 2015^24195 (mod 2017). You may use that 2017 is prime. Let m and n be two coprime positive integer numbers. Let a be integer such that gcd(a, mn) = 1. Show that a^lcm(phi(m), phi(n)) = 1 (mod mn), where lcm(phi(m), phi(m)) is the least common multiple of phi(m) and phi(n). Deduce that for any a which is coprime with 10, a^20 equiv 1(mod 100). With help of the previous section or otherwise find the last two digits of 7^(7^4) and of 7^(7^400).
Find 2015^24195 (mod 2017). You may use that 2017 is prime. Let m and n be two coprime positive integer numbers. Let a be integer such that gcd(a, mn) = 1. Show that a^lcm(phi(m), phi(n)) = 1 (mod mn), where lcm(phi(m), phi(m)) is the least common multiple of phi(m) and phi(n). Deduce that for any a which is coprime with 10, a^20 equiv 1(mod 100). With help of the previous section or otherwise find the last two digits of 7^(7^4) and of 7^(7^400).
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Beverley SmithLv2
9 Jun 2019