Two divisors of (n 2 +1)/2 summing up to n+1
Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 561-566.

Dans cette courte note, on donne une réponse affirmative à une question d’Ayad posée dans [1].

In this short note, we give an affirmative answer to a question of Ayad from [1].

Reçu le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.602
@article{JTNB_2007__19_3_561_0,
     author = {Mohamed Ayad and Florian Luca},
     title = {Two divisors of $(n^2+1)/2$ summing up to $n+1$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {561--566},
     publisher = {Universit\'e Bordeaux 1},
     volume = {19},
     number = {3},
     year = {2007},
     doi = {10.5802/jtnb.602},
     zbl = {1161.11004},
     mrnumber = {2388788},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.602/}
}
Mohamed Ayad; Florian Luca. Two divisors of $(n^2+1)/2$ summing up to $n+1$. Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 561-566. doi : 10.5802/jtnb.602. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.602/

[1] M. Ayad, Critical points, critical values of a prime polynomial. Complex Var. Elliptic Equ. 51 (2006), 143–160. | MR 2201670 | Zbl 1091.12001

[2] Yu. F. Bilu, B. Brindza, P. Kirschenhofer, A. Pintér and R. F. Tichy, Diophantine equations and Bernoulli polynomials. With an appendix by A. Schinzel. Compositio Math. 131 (2002), 173–188. | MR 1898434 | Zbl 1028.11016

[3] Yu. F. Bilu and R. F. Tichy, The Diophantine equation f(x)=g(y). Acta Arith. 95 (2000), 261–288. | MR 1793164 | Zbl 0958.11049

[4] Y. Bugeaud and F. Luca, On Pillai’s Diophantine equation. New York J. Math. 12 (2006), 193–217. | Zbl pre05074583