(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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