2020/06/15 by Neelima Borade, Borade, Neelima, Jacob Mayle +1
Mathematics · #11A63 (Primary) 11A07 #11G05 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2006.08083
openalex publication_date 2020/06/15 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
A curious number is a palindromic number whose base ten representation has the form a … a b … b a … a. In this paper, we determine all curious numbers that are perfect squares. Our proof involves reducing the search for such numbers to several single variable families. From here, we complete the proof in two different ways. The first approach is elementary, though somewhat ad hoc. The second entails studying integral points on elliptic curves and is more systematic.