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Because, otherwise in the preceding test the first integer k to be evaluated is 1, which trivially yields the integer N under test of 1th root. This is a false positive result that ought to be eliminated.
:"1 > k" might be a mistake for "1 < k". <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.15.21.214|82.15.21.214]] ([[User talk:82.15.21.214#top|talk]]) 10:54, 4 July 2019 (UTC)</small> <!--Autosigned by SineBot-->
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