The Generalized Nagell–Ljunggren Problem: Powers with Repetitive Representations

@article{Bridy2019TheGN,
  title={The Generalized Nagell–Ljunggren Problem: Powers with Repetitive Representations},
  author={Andrew Bridy and R. Oliver and Arlo Shallit and J. Shallit},
  journal={Experimental Mathematics},
  year={2019},
  volume={28},
  pages={428 - 439}
}
ABSTRACT We consider a natural generalization of the Nagell–Ljunggren equation to the case where the qth power of an integer y, for q ⩾ 2, has a base-b representation that consists of a length-ℓ block of digits repeated n times, where n ⩾ 2. Assuming the abc conjecture of Masser and Oesterlé, we completely characterize those triples (q, n, ℓ) for which there are infinitely many solutions b. In all cases predicted by the abc conjecture, we are able (without any assumptions) to prove there are… Expand
1 Citations

Topics from this paper

Waring's Theorem for Binary Powers

References

SHOWING 1-10 OF 73 REFERENCES
New bounds and conditions for the equation of Nagell–Ljunggren
Sur L'équation Diophantienne (xn−1)/(x−1)=yq, III
The equation formula here has no solution with x square
Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren
Linear Forms in two m-adic Logarithms and Applications to Diophantine Problems
Zeroless Positional Number Representation and String Ordering
  • R. Boute
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 2000
...
1
2
3
4
5
...