If $a$ and $b$ must be nonnegative integers, what is the largest integer $n$ such that $13a + 18b = n$ has no solutions? What I've tried so far: I've tried doing this problem with smaller primes (2,5 and 5,7) and manually found answers with a table. I couldn't generalize this. Where I'm stuck: $13a+18b=n$ So, $13a+13b=n-5b$ So, $13(a+b)=n-5b$ But I don't know how to find an $n$ that does not work.

Guest Dec 9, 2022

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Guest
Dec 9, 2022