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# Academic paper by Enrique Treviño, Richter Scholar, and Georgia professor published

A paper written by Associate Professor of Mathematics Enrique Treviño, Dipika Subramaniam ’21, and University of Georgia Associate Professor of Mathematics Paul Pollack was recently published in Integers, a refereed online journal devoted to number theory research.

“On Sums of Consecutive Triangular Numbers” began with Subramaniam’s 2018 Richter project, in which she spent the summer working with Treviño to answer the question of when consecutive triangular numbers can add up to another triangular number. A triangular number is a number that can be written as the sum of the first n positive integers for some n. For example, 6 is a triangular number since 6 = 1+2+3, and so is 10 = 1+2+3+4. The first few triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, so an example of consecutive triangular numbers adding up to a triangular number is 1 + 3 + 6 = 10.

“The paper proves that for any perfect square k, there are k consecutive triangular numbers that add up to a triangular number. The paper also proves that for most integers k, there aren’t k consecutive triangular numbers that add up to a triangular number,” Treviño said.

Upon completion of Subramaniam’s Richter project in 2018, Treviño and Pollack continued the research, which was published in Integers in April 2020.