A positive integer is called a squaresum if and only if it can be written as the sum of the squares of two integers. For example, 61 and 9 are both squaresums since $61 = 5 ^ { 2 } + 6 ^ { 2 }$ and $9 = 3 ^ { 2 } + 0 ^ { 2 }$.
A prime number is called awkward if and only if it has a remainder of 3 when divided by 4 . For example, 23 is awkward since $23 = 5 \times 4 + 3$.
A (true) theorem due to Fermat states that:
A positive integer is a squaresum if and only if each of its awkward prime factors occurs to an even power in its prime factorisation.
It follows that $5 \times 23 ^ { 2 }$ is a squaresum, since 23 occurs to the power 2 , but $5 \times 23 ^ { 3 }$ is not, since 23 occurs to the power 3 .
Which one of the following statements is not true?