Hi,
here's a "little" problem i found in a book about induction :
Let's f a function from the naturals integers N to N that satisfy:
* f(1) > 0
* f(m² + n²) = (f(m))² + (f(n))²
I've calculate f(m) for m = 0 to 20 and find f(m) = m for all these values, but how can we give a good induction proof of this fact, i don't know ? ...
Could someone help me, please ! ...
Apologize for my poor english . Thanks
Best regards