Find the solution

Number Theory Level 3

If $x$ and $y$ are positive integers, find the number of solution of the equation $3x + 5y = 1008$ .

The answer is 67.

1 solution

James Wong
Mar 26, 2016

$3x+5y=1008$
$y=\frac{1008}{5}$ - $\frac{3}{5}x$
As $x$ and $y$ are positive integers, both of them cannot be zero.
To make $y$ an integers, $x$ must be integers with unit digits $1$ or $6$
The arithmetic sequence is $=1+(6-1)(n-1)$
For $y=0,x=336$ , $1+5(n-1)=336$ , $n=68$
As $y$ cannot be $0$ , the answer is $n=68-1=**67**$