On triangular numbers which are sums of consecutive squares

AbstractIn a recent issue of the American Mathematical Monthly, H. E. Thomas, Jr. proposed the following Problem. Find all integer solutions (n, r) of the equation ∑i=1n i = ∑i=1n i2 In the present paper we solve Thomas's problem by proving the following: Theorem. The only integer solutions of the equation ∑i=1n i = ∑i=1n i2 are ∑i=1n i = ∑i=1n i2