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Zbl 0876.11015
Dabrowski, Andrzej
On the diophantine equation $x!+A=y\sp 2$. (English)
[J] Nieuw Arch. Wiskd., IV. Ser. 14, No.3, 321-324 (1996). ISSN 0028-9825

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 $|abc|\le N_0 (abc)^s$ holds, where $N_0(n): =\prod_{p|n} p$ denotes the radical of a nonzero integer $n$ [see {\it S. Lang}, Bull. Am. Math. Soc., New Ser. 23, 37-75 (1990; Zbl 0714.11034)].
[E.L.Cohen (Ottawa)]

MSC 2000:: *11D99 Diophantine equations
11A99 Elementary number theory

Keywords: diophantine equation involving factorials; Szpiro conjecture

Citations: Zbl 0714.11034

Cited in: Zbl 1171.11020 Zbl 1099.11016 Zbl 1081.11020 Zbl 1085.11023

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