Write a full solution.
1.) Let be an even number and an odd number such that . Find the value of using Euclidean algorithm.
2.) (same as last year) Prove that if and are prime numbers, then is also prime number.
3.) Find all positive integers such that
is a composite number.
4.) Let . Prove that has at least distinct prime factors.
5.) Let such that and . Prove that is a perfect square.
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