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Math Challenge II-B Number Theory 3.28

 
 
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Re: Math Challenge II-B Number Theory 3.28
by John Lensmire - Wednesday, March 22, 2017, 9:34 AM
 

We want to look at (integer) solutions to $$1!+2!+\cdots + x! = y^2.$$ (For clarity, if $x=1$ the left side is just $1!$, if $x=2$ it is $1!+2!$, etc.)

Examine the left side first, and see if you notice a pattern with the units digit. This should help narrow down the values of $x$ you need to examine.