Problem #3
This month's problem involves expressing a positive integer as the sum of
the squares of (at least two) consecutive positive integers. Some integers
can be expressed as such a sum in more than one way. For example, 365 =
132 + 142 = 102 + 112 +
122. [Note that if we had not required at least two terms, we
could have used 25 = 52 = 32 + 42.
- Find a positive integer that can be written as a sum of the squares of
(at least two) consecutive positive integers in three ways.
- What about four ways?