Tuesday, 14 October 2025

Exercise (1.1).10

Determine $\gcd (a, a^2)$ where a is a non-zero integer.


Given that $a^2 = a \times a$, than $a$ is a factor of $a^2$.

Furthermore, $a$ is the largest factor of $a$. Therefore the largest factor of both is $a$.

However, $a$ could be negative, so we take. the modulus.

$$\gcd (a,a^2) = \lvert a \rvert$$