I need a necessary and sufficient condition for a number to be algebraic over integers.
I got this on wikipedia see here
If $\alpha$ is an irrational number which is the root of an irreducible polynomial $f$ of degree $n>0$ with integer coefficients, then there exists a real number $A>0$ such that, for all integers $p$, $q$, with $q>0$, $$\left|\alpha-\frac{p}{q}\right|>\frac{A}{q^n}$$
Is the above condition necessary and sufficient both?
Any help would be highly appreciated.