Question

If $4x-17y=1$ & $x,y\le 500$, find how many positive integer solutions are possible?

• A. $29$
• B. $28$
• C. $27$
• D. Cannot be determined

Answer 1

The correct option is A $29$

$4x-17y=1$

Or $4x-1=17y$

Or $4x-1$ must be multiple of $17$ and $y$ and $x\le 500$

Max multiple of $17$ in the set $4x-1$ i.e.

$(3,7,11,.........1999)$

to be divisible by $17$ is $(17,34,\mathrm{51........1989})$

Using $AP$ formula we get $n=29$

Hence, the answer is $29.$