Question

1. If a, b, m, n are positive integers such that 1 < a < b < n and ma = nb.

Which is bigger, m or n? Explain.

Answer 1

$a,\ b,\ m,\ n$ are positive integers such that $1<a<b<n$ and $ma=nb$ .

Using $a<b$ , we have $nb =ma<mb$ .

Dividing $nb<mb$ by $b$ , we obtain $n<m$ .

Answer: $m$ is bigger than $n$ .