Three-square Theorem as an Application of Andrews Identity

where df{n) denotes the number of divisors of n, d = i (mod 4). In literature there are several proofs of (1) and (2). For instance, M. D. Hirschhorn [7; 8] proved (1) and (2) using Jacobi's triple product identity. S. Bhargava & Chandrashekar Adiga [4] have proved (1) and (2) as a consequence of Ramanujan's ^ summation formula [10]. Recently R. Askey [2] has proved (1) and also derived a formula for the representation of an integer as a sum of a square and twice a square. The authors [5] have derived a formula for the representation of an integer as a sum of a square and thrice a square. These works of Askey [2] and the authors [5] also rely on Ramanujan's ^¥x summation [10]. In 1951 P. T. Bateman [3] obtained the following formula for r3(n):