Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.4 - Page 190: 37



Work Step by Step

If the integer is even, write it as $2x$. Then, its square is $4x^2$ and it can be written as $4(x^2)$ so $x^2=m$. If the integer is odd, write it as $2y+1$. Then, the square is $4y^2+4y+1=4(y^2+y)+1$, so $m=y^2+y$ is valid.
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