Arithmetic (Number theory) Article - Reading Comprehension - the Term "unmakable numbers"

[shahar]

I see that the term "unmakable number" and especially the term "unmakable" is not fine English. So Is it slang?
What is the meaning?
I think that I know roughly definition, so if one can give me definition that can be clear to this term, I will be glad.
The source:

Buzz in when you think you know the answer

Aperiodical guest author Andrew Taylor writes about an intriguing piece of number theory which turns out to also be something else. How many ways are there of writing some natural number $n$ as the…

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[HallsofIvy]

I think your link makes that quite clear. The author is talking about integers, n, that can be written as the sum of squares of two integers, \(\displaystyle n= a^2+ b^2\). Such numbers are "makeable" while other numbers are "unmakeable". For example, \(\displaystyle 25=3^2+ 4^2\) is "makeable" while 20 is "unmakeable".
(I don't know why you say "unmakeable" is not a "fine English word". It is in the dictionary as meaning "something that cannot be made". Perhaps you couldn't find it because you spelled it wrong- it is "unmakeable", not "unmakable')