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The numbers three, four, and five can be implanted in the Pythagorean process (3=a, 4=b, 5=c) to equal a correct right triangle. But my question is, are there any more directly consecutive numbers that can be used in the Pythagorean Theorem to equal a functional right triangle?

Curious Fish
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    Direct consecutive numbers as in $3,4,5$ or $23,24,25$, the answer is no. $3,4,5$ is the only consecutive triplet that satisfies the pythagorean theorem $a^2+b^2=c^2$ – imranfat May 04 '18 at 01:11
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    \begin{eqnarray} a^2+(a+1)^2=(a+2)^2 \end{eqnarray} Now do the algebra. – Donald Splutterwit May 04 '18 at 01:13
  • As a side note, when the Pythagorean theorem is "extended", then you can go nuts like I did here :https://math.stackexchange.com/questions/505367/surprising-identities-equations/505421#505421 – imranfat May 04 '18 at 01:18

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