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The important part is that we're only interested in integer ("whole number") solutions. In this case, the Diophantine equation is
n = 5x + 3y
and we only care about cases where x and y are both integers. For example, if n were 11, we don't care about the solution x=1.6, y=1. We're only interested in the solutions like x=1, y=2.
Sherlock and The Beast
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The important part is that we're only interested in integer ("whole number") solutions. In this case, the Diophantine equation is
n = 5x + 3y
and we only care about cases where x and y are both integers. For example, if n were 11, we don't care about the solution x=1.6, y=1. We're only interested in the solutions like x=1, y=2.