On the congruence x1x2≡x3x4modq

For q prime we prove a new bound for the error term in the asymptotic formula for the congruence x1x2≡x3x4modq and as an application give a new bound for the 4-th moment of character sums. Our argument is based on and improves results of Ayyad, Cochrane and Zheng and Garaev and Garcia.