\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A natural integer \(n\) is such that if it is divided by \(5\), the remainder is \(3\). If it is divided by \(6\), the remainder increases by \(1\) and the quotient decreases by \(1\).
Determine \(n\).
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