Question

When positive integer n is divided by 5, the remainder is x. When 2n is divided by 5, the remainder is y. Which pair (x, y) is not possible?

Answer 1

answer is (3,2)

Answer 2

\(n \equiv x \mod 5\)
\(2n \equiv y \mod 5\)

\(\implies\)

\(2x \equiv y \mod 5\)

\(2x-y \equiv 0 \mod 5\)

Answer 3

or \(2x -y = 5k\)

Answer 4

so the conditions is :
\(2x-y\) needs to be exactly divisible by 5