Two exponential diophantine equations
Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 2, pp. 479-487.

The equation 3 a +5 b -7 c =1, to be solved in non-negative rational integers a,b,c, has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation y 2 =3 a +2 b +1, to be solved in non-negative rational integers a,b and a rational integer y, has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.

L’équation 3 a +5 b -7 c =1, dont les inconnues a,b,c sont des entiers positifs, a été mentionnée par Masser comme un exemple pour lequel il n’y a pas d’algorithme permettant une résolution complète. Malgré cela, nous trouvons ici toutes les solutions. L’équation y 2 =3 a +2 b +1, dont les inconnues a,b sont des entiers positifs et y est un entier, a été mentionnée par Corvaja et Zannier comme un exemple dont on ignore si le nombre de solutions est fini. Mais nous trouvons également ici toutes les solutions ; il n’y en a en fait que six.

DOI: 10.5802/jtnb.773
Dominik J. Leitner 1

1 Mathematisches Institut Universität Basel Rheinsprung 21 4051 Basel, Switzerland
     author = {Dominik J. Leitner},
     title = {Two exponential diophantine equations},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {479--487},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {23},
     number = {2},
     year = {2011},
     doi = {10.5802/jtnb.773},
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     language = {en},
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Dominik J. Leitner. Two exponential diophantine equations. Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 2, pp. 479-487. doi : 10.5802/jtnb.773.

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