Dąbrowski, Andrzej On the diophantine equation \(x!+A=y^ 2\). (English) Zbl 0876.11015 Nieuw Arch. Wiskd., IV. Ser. 14, No. 3, 321-324 (1996). For positive integers \(x,y,A\) (not a square), the diophantine equation in the title has at most finitely many solutions. If \(A\) is square, the finiteness of solutions is implied by a weak form of Szpiro’s conjecture; namely: there exists a constant \(s>0\) such that for any nonzero mutually prime integers \(a,b,c\) with \(a+b=c\), the inequality \(|abc|\leq N_0 (abc)^s\) holds, where \(N_0(n): =\prod_{p|n} p\) denotes the radical of a nonzero integer \(n\) [see S. Lang, Bull. Am. Math. Soc., New Ser. 23, 37-75 (1990; Zbl 0714.11034)]. Reviewer: E.L.Cohen (Ottawa) Cited in 4 ReviewsCited in 10 Documents MSC: 11D99 Diophantine equations 11A99 Elementary number theory Keywords:diophantine equation involving factorials; Szpiro conjecture Citations:Zbl 0714.11034 PDFBibTeX XMLCite \textit{A. Dąbrowski}, Nieuw Arch. Wiskd., IV. Ser. 14, No. 3, 321--324 (1996; Zbl 0876.11015)