benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / In base 10, the number 2013 ends in the digit 3. In base 9, on the other hand, the same number is written as (2676)₉ and ends in the digit 6. For how many values of b does the base…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In base 1010, the number 20132013 ends in the digit 33. In base 99, on the other hand, the same number is written as (2676)9(2676)_{9} and ends in the digit 66. For how many values of bb does the base-bb-representation of 20132013 end in the digit 33?
Plain-text mathematical notation (without MathML)
In base 10, the number 2013 ends in the digit 3.  In base 9, on the other hand, the same number is written as (2676)₉ and ends in the digit 6.  For how many values of b does the base-b-representation of 2013 end in the digit 3?
Original LaTeX notation
In base $10$, the number $2013$ ends in the digit $3$.  In base $9$, on the other hand, the same number is written as $(2676)_{9}$ and ends in the digit $6$.  For how many values of $b$ does the base-$b$-representation of $2013$ end in the digit $3$?

level

Level 5

type

Number Theory

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
7e4873d8-9506-5585-9194-3037f1a07439
task_key
number~5ftheory--test--7e4873d8-9506-5585-9194-3037f1a07439
task_revision_id
1
config / split
number_theory / test

Official source

initial import