Perfect factorials
Number Theory
Level
3
The number of value(s) of for which is a perfect square.
0
6
2
1
None of these.
3
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1 solution
First, we notice that for factorials greater than 5! the last digit will be 0. So we can calculate the earlier cases since there are only 4... 1!=1 ok
1!+2!= 3 no
1!+2!+3!=9 ok
1!+2!+3!+4!=33 no
From now on the last digit will be forever 3, because of the observation I made above. But 3 isn't the last digit of any perfect square, so the only suitable numbers are 1 and 3.