Question: (a) You are given that p 4 is a prime number and that 3p4 1 (mod p). Find all values p with such properties. (b)

(a) You are given that p 4 is a prime number and that 3p4 1 (mod p). Find all values p with such properties.

(b) Let a, b, n be integer numbers such that gcd(a, b) = 1. Show that: if a | n and b | n then ab | n. You may use any results which were proven in lectures

(c) Find an integer number n such that 5n is a fifth power of some integer number, 6n is a sixth power of some integer number and 7n is a seventh power of some integer number. [Hint: Consider the prime factorisation of n. If your answer is huge you do not have to write its decimal expansion. You may leave it as a mathematical expression.]

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