Yeah that sounds more correct, thank youThink you meant:
prove that x is a Fibonacci number if and only if 5x^2+4 or 5x^2-4 is a perfect square. (just being picky).
i might have a quicker way and easier to find,We know that:
Now let and
Multiply both sides by 3 to establish the inequality:
Now consider:
Split the RHS up into the following:
Now using the inequality we establish before, we get:
Let this be A:
Hence since
Yep that is correct.
Maybe not quite correct yet. May need to have a look at it again
First post, let's see if I can get the latex right -- I'm studying how you've done it lol
The first answer is correct, as for the second one, let me check my proof again, I got the result from 'Art of Problem SOlving' and it asked whether it diverged and converged.First post, let's see if I can get the latex right -- I'm studying how you've done it lol
Are you sure this one is correct? I'm fairly certain I can prove it has a lower bound of 9 and an upper bound of 90 pretty easily...
Is it (-1)^n-1*n!*k^n???Another good Putnam question
I thought so too, its problem A1 for 2002 iirc.seemed a bit on the easy side for putnam surely???