MathNet 2010 — Part 04 Question 129

The polynomial $A(x)=x^{2}+a x+b$ with whole coefficients has the property that for each prime $p$ there is an integer $k$ so that $A(k)$ and $A(k+1)$ Both can be divided by $p$. Prove that an integer $m$ exists so that $A(m)=A(m+1)=0$.