solution to an equation involving natural numbers Suppose $a,b$ are real numbers and we have 
$$ 1 = b + an \; \; \; \; \forall n \in \mathbb{N} $$
My book says that only solution is $b=0$, $a=1$. But, this does not make sense to me since if we put $n = 1$, we have 
$$ 1  = b + a $$
And $a=b=1/2$ is a solution. What is wrong?

For all $n$ implies that we have:
$$1=b+a$$
$$1=b+2a$$
So $a=0$ and $b=1$ is the only solution.
