How to Prove that (n-1)!= 0 (mod n) for Composite n?

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dessy
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If n is composite, n>4, prove that (n-1)!= 0 (mod n). = is congruent
 
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Let n=(n-i)(n-j). If i is not equal to j then both terms will appear in the expansion of (n-1)!. You can probably handle the case i=j yourself with a little thought.
 

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