Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Question

Prove the following statements using direct, contrapositive, or contradiction proof:

a.  If n is an integer, then 4 | n^2 or 4 | [(n^2) + 1].

b. The product of any n consecutive positive integers is divisible by n!.

c. Suppose a,b, and p are integers and p is prime. Prove that if p | ab then p | a or p | b.

d.  If n is an integer, then gcd(n,n + 2) = {1,2}.

e.  Suppose a, and b are integers. Then a = lcm(a,b) if and only if b | a.

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