Note on Indeterminate Equations

Let a₁x₁+a₂x₂= n be an indeterminate equation of the first degree in two unknowns x₁, x₁. To find ihe number of solutions of this equation in integers, zero values being included, we may proceed a follows :-

Denote by I₁(n) the number of integral solutions of the equation a₁x₁=n.