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引用次数: 1
摘要
抽象让年代(n)的非零位二进制数字整数n。我们研究的扩张,固定k,ℓ,m,丢番图系统s (ab) = k s (a) =ℓ,和s (b) = m在奇数变量,b.When k = 2或k = 3,我们建立一个绑定abℓ和m。在这样一个绑定不存在k = 4的情况下,我们给一个上界最小{a、b}ℓ和m。
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.
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