In this article, given a number P ∈ N that ends in one and assuming that there are integer solutions (A; B) ∈ N × N for the equations P = (10x + 9)(10y + 9) or P = (10x + 7)(10y + 3) or P = (10x + 1)(10y + 1), the straight line was used passing through the center of gravity of the triangle bounded by the vertices (A; A), (B; A), (A; B). Considering A ≥ 25, we manage to divide the domain of the curve P = (10x + 9)(10y + 9) into two disjoint subsets, and using Theorem (2.2) of this article, we find the subset where the integer solution of the equation P = (10x + 9)(10y + 9) is found. Similar process is done when P = (10x + 1)(10y + 1), in case P is of the form P = (10x + 7)(10y + 3) or P = (10x + 3)(10y + 7). These curves are different and to obtain a process similar to the one carried out previously, we proceeded according to Observation 2.2. Our results allow minimizing the number of operations to perform when our problem requires to be implemented computationally.Furthermore, we obtain some conditions to find the solution of the equations: