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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?

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  1. 14 December, 00:14
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    Any integer that is not integer multiple of 234 is not a solution.

    Step-by-step 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.
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