Question

If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?

Answer 1

Any integer that is not integer multiple of 234 is not a solution.

Explanation:

We are required to find the largest integer n such that 13a + 18b = n has no solution, where a and b are integers.

13a + 18b = n

For a = 1, b = 0

n = 13

For a = 0, b = 1

n = 18

So, for the solution sets (1, 0), (0, 1), n will always have a solutions.

Consider n = 13 × 18 = 234

This means that any integer that is not integer multiple of 234 is not a solution.