MathDB

An integer

n

is called

k

-special, with

k

a positive integer, if it's the sum of the squares of

k

consecutive integers. For example,

13

2

-special, since

13=2^2+3^2

, and

2

3

-special, since

2=(-1)^2+0^2+1^2

.
a) Prove that there's no perfect square that is

4

-special.
b) Find a perfect square that is

I^2

-special, for some odd positive integer

I

with

I\ge 3

Problem Statement