MathDB

exists n such that the k-th digit from the right of 2^n is d

Source: Mathcenter Contest / Oly - Thai Forum 2010 R1 p2 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 15, 2022

number theoryDigitspower of 2

Problem Statement

Let

k

and

d

be integers such that

k>1

and

0\leq d<9

. Prove that there exists some integer

n

such that the

k

th digit from the right of

2^n

d

.
(tatari/nightmare)