2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75814In this paper Euler shows that there are no additional square idoneal numbers aside from 1, 4, 9, 16, and 25.4 pages, seems to be first English translation of Latin original ``Illustratio paradoxi circa progressionem numerorum idoneorum sive congruorum'', Nova Acta Academiae Scientarum Imperialis Petropolitinae 15 (1806), 29-32, E725History and OverviewNumber Theory01A50; 11A41text