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Abstract
This work is devoted to proving that, given an integer
x
≥ 2 ,
there are infinitely many perfect powers coprime with
x having exactly
k
≥ 3 nonzero digits in their
base
x representation,
except for the case
x
= 2 ,
k
= 4 , for
which a known finiteness result by Corvaja and Zannier holds.
Keywords
sparse powers, base representation
Mathematical Subject Classification
Primary: 11P99
Secondary: 11D41
Milestones
Received: 25 January 2021
Revised: 25 July 2021
Accepted: 11 September 2021
Published: 17 January 2022