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Problem

Consider the iterative formula, $u$_$n$+1 = $u$_$n$ + 2. By investigating the behaviour it should become clear that all positive starting values converge to the limit 4.

What form must the positive integer, $m$, take, for the iterative formula, $u$_$n$+1 = $u$_$n$ + $m$, to converge to an integral root?