Question

Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways. (Use a computer or calculator to speed up your work.)

Short answer

18 is a possible positive integer for which the statement is true.

Step-by-step solution

Describe the given information

There is a positive integer that can be written as the sum of square of positive integers.

Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways

The square of positive integers is \(1,\;4,\;9,\;16,\;25,...\).

The number 18 can be written as the two different sums of squares of positive integers:

\(\begin{array}{c}18 = 9 + 9\\18 = 4 + 4 + 4 + 4 + 1 + 1\end{array}\)

Therefore, 18 is a positive integer for which the to be proven statement is true.