MathDB

Positive integer

d

is not perfect square. For each positive integer

n

, let

s(n)

denote the number of digits

1

among the first

n

digits in the binary representation of

\sqrt{d}

(including the digits before the point). Prove that there exists an integer

A

such that

s(n)>\sqrt{2n}-2

for all integers

n\ge A

Problem Statement