# A divisibility problem 2

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• February 27th 2010, 03:40 PM
eyke
A divisibility problem 2
Show that $(n!+1, (n+1)!+1)=1$
• February 27th 2010, 04:32 PM
NonCommAlg
Quote:

Originally Posted by eyke
Show that $(n!+1, (n+1)!+1)=1$

if $d \mid n! + 1,$ then $d \mid (n+1)! + n+1.$ so if we also have $d \mid (n+1)! + 1,$ then $d \mid n$ and hence $d \mid n!,$ which completes the proof because we're given that $d \mid n!+1.$