# 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

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