2011/088) Find a right angled triangle with integer sides whose all three sides are fibonacci numbers.

No solution

Proof:

Let the legs be x and y

X and y cannot be same then hypotenuse shall be x qrt(2) and it is not integer.

Now let x < y and so hypotenuse >= (x+y)

as next Fibonacci number = (x+y) if x and y are consecutive Fibonacci numbers

and > (x+y) if they are not consecutive

So x^2+y^2 >= (x+y)^2 which is not possible unless x = 0

Hence no solution