Can we find the count of all pythogorean triplets in range a to b which are natural numbers.

eg if a = 1 b = 10 then count will be 2 because of (3,4,5) and (6,8,10)

Edit: Can we directly make a formula for it?

  • $\begingroup$ Please define objects. What does it mean that a triple like $(3,4,5)$ is placed between $1$ and $10$? What means that we "can find the count"?! Should we find an explicit formula which is generally valid for all $a$ (start of the interval) and $b$ (end of the intreval)? (The letters $a,b$ are nicely used for the range in connection with pythagorean triples... how shall we denote such a triple?! Is it not enough to take $a=1$?!) Please show the own work... $\endgroup$ – dan_fulea Mar 26 at 4:22
  • $\begingroup$ Look for (m,n) such that $2mn$ and $n^2-m^2$ are greater than lower limit and $n^2+m^2$ is smaller than the higher limit. $\endgroup$ – Moti Mar 26 at 6:23

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