How to prove that the distance between the origin and the point $P$ is a natural number, where $P=(n, n+1, n(n+1))$.
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Origin in which space? Do you mean $p=P$? What did you try yourself? – Dietrich Burde Aug 19 '18 at 13:10

$\mathbb{R}^3$ with Euclidean norm I guess – Jakobian Aug 19 '18 at 13:11

what is the value n? – user144410 Aug 19 '18 at 13:13

R³, origin O = (0,0,0). – jofernando Aug 19 '18 at 13:16

1Do you know how to compute the distance? – Arnaud D. Aug 19 '18 at 15:26
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The distance is $$\sqrt{n^2+(n+1)^2+(n(n+1))^2}=\sqrt{(n^2+n)^2+2(n^2+n)+1}=\sqrt{(n^2+n+1)^2}=n^2+n+1$$
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