How many natural numbers $n≤1000$ cannot be written in the form $a^2−b^2−c^2 \ ;$
where $a$,$b$ and $c$ are non-negative integers subject to condition $a≥b+c$.
How to approach?
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All negative integers $n$ cannot be written in that form. I assume you mean $n \geq 0$? – Ivan Loh Mar 30 '13 at 09:17
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@IvanLoh Done Editing ! Well it was correct in header. – ABC Mar 30 '13 at 09:20
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1https://brilliant.org/i/8SEjnB/ – lab bhattacharjee Mar 30 '13 at 16:58
1 Answers
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HINT:
$2n+1=(n+1)^2-n^2-0^2 ;a=n+1,b=n,c=0$
$2n=(n+1)^2-n^2-1^2 ;a=n+1,b=n,c=1$
lab bhattacharjee
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The pattern can be easily identified by testing up to some integers $n:a,b,c; 1:1,0,0;2:2,1,1;3:2,1,0;4:3,2,1;5:3,2,0;6:4,3,1;7:4,3,0;8:5,4,1;9:5,4,0;10:6,5,1;$ – lab bhattacharjee Mar 30 '13 at 09:43