Question: 1. Prove that there exist no integers a and b for which 4a + 10b = 1. 2. Let p be a prime number.

1. Prove that there exist no integers a and b for which 4a + 10b = 1. 2. Let p be a prime number. Use

1. Prove that there exist no integers a and b for which 4a + 10b = 1. 2. Let p be a prime number. Use contradiction to prove that p is irrational. You may assume the following fact: If a, b = Z and p|(ab), then pla or p/b.

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