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What is the smallest positive integer n such that the rightmost three digits of n and n + n! are the same?

 Oct 27, 2021
 #1
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What is the smallest positive integer n such that the rightmost three digits of n and n + n! are the same?  

 

I don't know, but my first thought was 1000.  Those three zeroes would always be on the end. 

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 Oct 27, 2021
 #2
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n = 100 does the trick.

 

(if we allow preceding zeros for n, then n = 015 works.  015+015! = 1307674368015)

 Oct 29, 2021

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