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Prove that if n is a positive integer greater than 1 such that n is not a prime, then n has a divisor d such that 1dn.
Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that a2=3b2. Explain how this proves that 3 is not a rational number.
Prove that if p and q are distinct primes, then there exist integers m and n such that pm+qn=1.
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