ON THE DIGITAL REPRESENTATION OF INTEGERS WITH BOUNDED PRIME FACTORS To Noriko Hirata-Kohno on her sixtieth birthday

摘要

Let b = 2 be an integer. Not much is known on the representation in base b of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of b and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base b.