Find the smallest right triangle with integer sides such that the hypotenuse is a square and the sum of the legs is also a square.
If the triangle has sides a,b,c
where c (hypotenuse) is the square of integer n
and a+b is the square of integer m:
a^2 + b^2 = n^4
and a+b = m^2
I could not find any solutions; I suspect there are no integer solutions.
Putting "x^2 + y^2 = n^4 integers" into Wolfram Alpha finds only (0,0,0)

Posted by Larry
on 20240102 08:26:29 