The expression seems familiar...

Number Theory Level pending

Consider the set,

$S$ $=$ { $ax$ $+$ $by$ $|$ $x,y \in \mathbb{Z}, ax + by>0$ }

Find the smallest element in $S$ for $a=5313$ and $b=2024$ .

1 solution

Rajen Kapur
Apr 16, 2014

gcm(5313,2024)=253 and taking it out as common we find (-3) x 21 + 8 x 8 = 1, to claim 253 as the answer.