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## Parity and Symbolic Divisibility – an excursion in Number Theory

Consider the following problem: Problem Show that there do no exist non-negative integers k and m such that $$k! + 48 = 48(k+1)^m$$ Discussion Claim 1: $$k \geq 9$$ If there are such integers then $$k! = 48 \times ((k+1)^m – 1 )$$. Expanding we have \( k! =...