Problem #418

Into the 4th dimension
Public 09/01/17 5xp Math 70.0%

Consider a sphere whose square of its radius is $n$ and centered at $(0,0,0,0)$ in the $4^{th}$ dimension space.
For a given $n$, the sphere touches a certain number of integer lattice points.

For instance, if $n = 7$, it touches the point (1,2,1,1)

Let $t(n)$ the number of integer lattice points touched by the sphere with square of radius $n$

Find $\sum_{k=0}^{100}t(10^{17}+k)$

You are given $\sum_{k=0}^{100}t(1000+k)=1042664$

[My timing: 9 sec]



You need to be a member to keep track of your progress.
Register


Time may end, but hope will last forever.

Other Challenge Sites

Contact

elasolova
[64][103][109][97][105][108][46][99][111][109]