Finding the Smallest n for F(n)=24: A Challenge in Integer Solutions

[pi_kid]

I'm having some trouble with a particular question brought up in class. It says given F(n)= to the total # of integer solutions what is the smallest n such that F(n)=24. I know how to find F(n) given n, but i can't figure out how to work backwards. Any hints would help.

 

[mathman]

"integer solutions" to what?

 

[galoisjr]

By sums of squares it depends on the amount of terms your adding. There is no answer for 2 squares to equal 24 but for 3 squares there's 4^2+2^2+2^2 and then for 6 squares it could be 2^2+2^2+2^2+2^2+2^2+2^2 so i would guess 2? Please fully explain the problem though.