Products of Integers with Few Nonzero Digits
Hajime Kaneko, Thomas Stoll · Uniform distribution theory · 2022
Abstract Let s ( n ) be the number of nonzero bits in the binary digital expansion of the integer n . We study, for fixed k, ℓ, m , the Diophantine system s ( ab )= k, s ( a )= ℓ, and s ( b )= m in odd integer variables a, b .When k =2 or k = 3, we establish a bound on ab in terms of ℓ and m . While such a bound does not exist in the case of k =4, we give an upper bound for min{ a, b } in terms of ℓ and m .