Question

The number of ways to select $2$ numbers from {$0,1,2,3,4$} such that the sum of the squares of the selected numbers is divisible by $5$ are (repetition of digits is allowed).

Answer 1

Select 2 numbers from {0,1,2,3,4} $\to (a,b)$

Such that $a^2+b^2$ is divisible by 5.

$a=0,b=0$ $a^2+b^2=0$

$a=1,b=2$ $a^2+b^2=5$

$a=2,b=1$ $a^2+b^2=5$

$a=3,b=1$ $a^2+b^2=10$

$a=1,b=3$ $a^2+b^2=10$

$a=2,b=4$ $a^2+b^2=20$

$a=5,b=0$ $a^2+b^2=25$

$a=0,b=5$ $a^2+b^2=25$

Total ways =9