You need two simple calculations

Number Theory Level 3

Let $A$ and $B$ be non-negative integers.

$C$ is the largest integer that CANNOT be expressed in the form $13A + 18B$

There is only one pair of integers $F, G$ both greater than 1 such that $C = F * G$

Assume $F < G$ .

What is $G - F$ ?

1 solution

Denton Young
Dec 30, 2019

If H, J are relatively prime, the largest number that cannot be expressed as a combination of multiples of H and J is (H*J) - H - J

(13 * 18) - 13 - 18 = 234 - 31 = 203

203 = 7 * 29

29 - 7 = 22