Elements Of Modern Algebra

8th Edition

ISBN: 9781285463230

Author: Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

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Prove that if p is a prime, then the square root of p is irrational.

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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.

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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.

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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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