We will prove these conjecture. These are very interesting because, as Dense points out in his article [2], they "bear strong resemblance to a known identity,". Dense found the equation (1) in Section 6.4, Exercises 1-3, pp. 89-90 [1]. Secondly, Dense seems to have arrived at these conjectures by way of a novel application of the Laplace transform. We will prove an identity in the next theorem for which the conjectures are special cases with additional work. Theorem. For any real or complex numbers x and y, and for any positive integer n. This is a curious result. It is almost too good to be true since it says that the left hand side of the equation is independent of the choice of the number y, We use elementary methods to prove the theorem and the conjectures.