Solutions to the Diophantine Equation x(2)

We present a method of determining integral solutions to the equation x(2) + 16 . 7(b) = y(2r), where x, y, b,r is an element of Z(+). We observe that the results can be classified into several categories. Under each category, a general formula is obtained using the geometric progression method. We then provide the bound for the number of non-negative integral solutions associated with each b. Lastly, the general formula for each of the categories is obtained and presented to determine the respective values of x and y(r). We also highlight two special cases where different formulae are needed to represent their integral solutions.