Talk:Numbers Not Expressible as Sum of no more than 5 Squares of Composite Numbers

A misprint in both Guy and Wells.

All numbers $>1$ can be expressed as a sum of multiples of $2$ and $3$:

$\forall x > 1: \exists s, t \in \N: x = 2 s + 3 t$

Hence for all $x > 11$:

$x = 2 \paren {s + 2} + 3 \paren {t + 2}$

so all numbers $> 11$ is the sum of two composite numbers.

The section in question is C20 Sum of Squares, so it should be interpreted as such:

Apart from $256$ examples, the largest of which is $1167$, every number can be expressed as the sum of at most five [squares of] composite numbers[, allowing repetition].

However the sequence A055075 on OEIS gives no insight into which $256$.

Neither does the source material, E3262 of Amer. Math. Monthly. --RandomUndergrad (talk) 14:47, 28 July 2020 (UTC)

I've just checked my copy of Edition 2 of Guy:

Apart from $256$ examples, the largest of which is $1167$, every number can be expressed as the sum of at most five squares of composite numbers.

So I'll rename and redraft this, add a Historical Note, and add a page to the Wells errata list. --prime mover (talk) 15:50, 28 July 2020 (UTC)

There, the errata pages have been done. --prime mover (talk) 16:22, 28 July 2020 (UTC)