# Close Enough

Except when the prime factors of `a, b`

already co-operate, the iron hand of the Fundamental Theorem of Arithmetic dictates that the integer powers `a**pa`

and `b**pb`

can never be equal for any two positive integer exponents `pa`

and `pb`

. However, in the jovial spirit of “close enough for government work”, we define two such powers to “hit” if their difference `abs(a**pa-b**pb)`

multiplied by the `tolerance`

is at most equal to the smaller of those powers. (This definition intentionally avoids division to keep it both fast and accurate for arbitrarily large integers.) For example, `tolerance=100`

expects `a**pa`

and `b**pb`

to be within 1 %.

For given positive integers `a, b`

return the smallest positive integer exponents `(pa, pb)`

that satisfy the `tolerance`

requirement.

**Input:** Three integers (int).

**Output:** Tuple (or list) of two integers (int).

**Examples:**

assert list(hitting_powers(9, 10, 5)) == [1, 1] assert list(hitting_powers(2, 4, 100)) == [2, 1] assert list(hitting_powers(2, 7, 100)) == [73, 26] assert list(hitting_powers(3, 6, 100)) == [137, 84]

*The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen*

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin

checkio install-plugin --ff

checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.