1. ## arithmetic

hello,

Prove that $\forall n \in \mathbb{N}$ , there's no number $k\in \mathbb{N}$ and $3n^2 + 3n +7= k^3$

2. Originally Posted by linda2005
hello,

Prove that $\forall n \in \mathbb{N}$ , there's no number $k\in \mathbb{N}$ and $3n^2 + 3n +7= k^3$
i haven't worked out the details, but a proof by contradiction should work. assume there is such a k. what would the solution to $3n^2 + 3n + 7 - k^3 = 0$ look like? would $n$ be a natural number or even an integer at all? try the quadratic formula, see what happens