Online Course Discussion Forum

Math Challenge II-B Number Theory 3.28

 
 
Picture of Laura Wu
Math Challenge II-B Number Theory 3.28
by Laura Wu - Wednesday, 22 March 2017, 5:30 AM
 

Can you please offer a hint to this problem? I have no idea how to go about it. Thank you!

 
Picture of John Lensmire
Re: Math Challenge II-B Number Theory 3.28
by John Lensmire - Wednesday, 22 March 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.