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

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

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

Received:
Published online:
DOI: 10.5802/jtnb.602
Mohamed Ayad 1; Florian Luca 2

1 Laboratoire de Mathématiques Pures et Appliquées Université du Littoral F-62228 Calais, France
2 Florian Luca Instituto de Matemáticas Universidad Nacional Autonoma de México C.P. 58089, Morelia, Michoacán, México
@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/}
}
TY  - JOUR
TI  - Two divisors of $(n^2+1)/2$ summing up to $n+1$
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2007
DA  - 2007///
SP  - 561
EP  - 566
VL  - 19
IS  - 3
PB  - Université Bordeaux 1
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.602/
UR  - https://zbmath.org/?q=an%3A1161.11004
UR  - https://www.ams.org/mathscinet-getitem?mr=2388788
UR  - https://doi.org/10.5802/jtnb.602
DO  - 10.5802/jtnb.602
LA  - en
ID  - JTNB_2007__19_3_561_0
ER  - 
%0 Journal Article
%T Two divisors of $(n^2+1)/2$ summing up to $n+1$
%J Journal de Théorie des Nombres de Bordeaux
%D 2007
%P 561-566
%V 19
%N 3
%I Université Bordeaux 1
%U https://doi.org/10.5802/jtnb.602
%R 10.5802/jtnb.602
%G en
%F JTNB_2007__19_3_561_0
Mohamed Ayad; Florian Luca. Two divisors of $(n^2+1)/2$ summing up to $n+1$. Journal de Théorie des Nombres de Bordeaux, Volume 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

Cited by Sources: