Question

Find the greatest value of $c$ in order that the equation $14x+11y=c$ may have exactly five solutions in positive integers.

Answer 1

The greatest value of $c=(n+1)ab-a-b=6\times 14\times 11-14-11=899$

Here, $n=$ no of solutions

$a$ and $b$ are coefficents of $x$ and $y$ respectively