Not So Obvious!

Number Theory Level 3

True or False?

$\quad$ $a|b$ and $b|a$ implies that $a=b$ .

Notation: Here $a$ and $b$ are integers. And $a|b$ means, $a$ divides $b$ , that is, there exists another integer $c$ such that $b=ac$ .

False True

1 solution

Muhammad Rasel Parvej
Nov 28, 2016

As an counter example, $4|(-4)$ and $(-4)|4$ , but $4 \neq (-4)$ . Yes, all the counterexamples are of the same kind to it.

The whole truth is : " $a|b$ and $b|a$ " implies that " $a=b$ or $a=-b$ ".