# Math Help - Proving that an expression is a perfect square for a finite number of values of n

1. ## Proving that an expression is a perfect square for a finite number of values of n

Prove that is the only integer making a perfect square

2. What about n=0 and n=-1?

--Kevin C.

3. True. Ok for 0 and 3 then..

4. ## Interesting problem indeed

Conjecture: The only integer solutions to the function $f(x)=\sqrt{x^4+x^3+x^2+x+1}$ are $(-1,1)$, $(0,1)$, and $(3,11)$. No others exist. Furthermore, $\lim_{|n|\rightarrow \infty} frac(f(n))=\frac{7}{8}$ for n odd and $\frac{3}{8}$ for n even, when $n \in \mathbb{Z}$.

I agree, it is an interesting problem, and looking at it numerically, I believe it to be true. But why these three solutions should exist uniquely, I do not know.

5. UPDATE: http://www.mathhelpforum.com/math-he...duction-3.html Proof for general case found a posteriori.