On a conjecture of Graham on the p$p$‐divisibility of central binomial coefficients
Copyright policy )On a conjecture of Graham on the p$p$‐divisibility of central binomial coefficients
AbstractLet be pairwise distinct primes. From a theorem of Kummer, each prime can divide at most times. We show that, for all , if are sufficiently large in terms of and , then there exist infinitely many positive integers such that each divides at most times. We connect this result to a famous conjecture by Graham on whether there are infinitely many integers such that is coprime to 105.
- Georgia Institute of Technology United States
- University of Bristol United Kingdom
- Mississippi School for Mathematics and Science United States
Distribution functions associated with additive and positive multiplicative functions, Mathematics - Number Theory, Binomial coefficients; factorials; \(q\)-identities, FOS: Mathematics, Mathematics - Combinatorics, Diophantine approximation in probabilistic number theory, Number Theory (math.NT), Combinatorics (math.CO), central binomial coefficient, 510, carries in addition in base \(p\)
Distribution functions associated with additive and positive multiplicative functions, Mathematics - Number Theory, Binomial coefficients; factorials; \(q\)-identities, FOS: Mathematics, Mathematics - Combinatorics, Diophantine approximation in probabilistic number theory, Number Theory (math.NT), Combinatorics (math.CO), central binomial coefficient, 510, carries in addition in base \(p\)
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