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oai:tokushima-u.repo.nii.ac.jp:02008866 2025-04-28T08:02:57Z 1713829974766:1713854679917:1716360590330 1713853213384:1713853297799

On Polygonal Square Triangular Numbers 70194777 片山, 真一 カタヤマ, シンイチ Katayama, Shin-ichi 片山 カタヤマ Katayama 真一 シンイチ Shin-ichi フルヤ, ナオキ フルヤ, ナオキ Furuya, Naoki ニシオカ, ユウキ ニシオカ, ユウキ Nishioka, Yuki open access A pentagonal square triangular number is a number which is a pentagonal number P5(ℓ), a square y2 and a triangular number P3(m) at the same time. It would be well known for the specialists that there exists no pentagonal square triangular number except for P3(1) = 12 = P5(1) = 1. But we don’t know any simple reference of the proof of this fact in print. The object of this note is to provide a such reference. Here we shall present three independent proofs of this fact one of which was already referred in the net article [24]. TOKUSHIMA UNIVERSITY 2020 eng departmental bulletin paper VoR 373586 https://tokushima-u.repo.nii.ac.jp/records/2008866 13467387 AA11595324 Journal of Mathematics 54 1 12 https://tokushima-u.repo.nii.ac.jp/record/2008866/files/jm_54_1.pdf application/pdf 363 KB 2021-05-11