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(b) The product of four consecutive integers is 1 less than a perfect square. 9. Establish that the difference of two consecutive cubes is never divisible by 2. 10. For a nonzero integer a, show that gcd (a, 0) = |a|, gcd(a, a) = | a |, and gcd(a, 1) = 1. 11. If a and b are integers, not both of which are zero, verify that

(b) The product of four consecutive integers is 1 less than a perfect square. 9. Establish that the difference of two consecutive cubes is never divisible by 2. 10. For a nonzero integer a, show that gcd (a, 0) = |a|, gcd(a, a) = | a |, and gcd(a, 1) = 1. 11. If a and b are integers, not both of which are zero, verify that

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 77E
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(b) The product of four consecutive integers is 1 less than a perfect square. 9. Establish that the difference of two consecutive cubes is never divisible by 2. 10. For a nonzero integer a, show that gcd (a, 0) = |a|, gcd(a, a) = | a |, and gcd(a, 1) = 1. 11. If a and b are integers, not both of which are zero, verify that
Transcribed Image Text:(b) The product of four consecutive integers is 1 less than a perfect square. 9. Establish that the difference of two consecutive cubes is never divisible by 2. 10. For a nonzero integer a, show that gcd (a, 0) = |a|, gcd(a, a) = | a |, and gcd(a, 1) = 1. 11. If a and b are integers, not both of which are zero, verify that
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