13 December, 23:48
If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?
14 December, 00:14
Any integer that is not integer multiple of 234 is not a solution.
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.
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» If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?