any two squares number whose square is a square
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no
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How do you find a number that is the sum of two squares and whose square is also the sum of two squares?
Jace Wayland
Answered 1 year ago
Let a be the required number such that a,b,c,d,e∈Z
Then we can form two equations:
a=b²+c²,
a²=d²+e²
The second equation can be satisfied by Pythagorean Triples and, off the top of my head, I say (3,4,5) is such a triple
3²+4²=5²
So a=5
⇒5=b²+c²
And it’s obvious that 1 and 2 satisfy the above equation
So one such number is 5
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