Question

Find the value of $r$ for any positive integer $a$ and $3$, there exist unique integer $q$ and $r$ such that $a=3q+r$.

Answer 1

Consider the problem

For any positive integer $a$ and $3$, by Euclid's division lemma We have,

$a=3q+r$

Where, $r=0$ Or $1$ Or $2$