Checking Perfect Power

Checking Perfect Power


A positive integer n is a perfect power if it can be expressed as the power be for some two integers b and e that are both greater than one. (Any positive integer n can always be expressed as the trivial power n1, so we don’t care about those.) For example, the integers 32, 125 and 441 are perfect powers since they equal 25, 53 and 212, respectively.

This function should determine whether the positive integer n is a perfect power. Your function needs to somehow iterate through a sufficient number of possible combinations of b and e that could work, returning True right away when you find some b and e that satisfy be == n, and returning False when all relevant possibilities for b and e have been tried and found wanting.

Since n can get pretty large, your function should not examine too many combinations above and beyond those that are both necessary and sufficient to reliably determine the answer. Achieving this efficiency is the central educational point of this problem.

Input: Integer (int).

Output: Logic value (bool).


assert perfect_power(8) == True
assert perfect_power(42) == False
assert perfect_power(441) == True
assert perfect_power(469097433) == True


  • n > 0.

Related to the mission, you may be interested at Catalan’s conjecture, these days a proven mathematical theorem that says that after the special case of the two consecutive perfect powers 8 and 9, whenever a positive integer n is a perfect power, n – 1 is never a perfect power. For example, we don’t have to slog through all potential ways to express the number as an integer power to know from the get-go that 1234567890-1 is not a perfect power. This also illustrates the common asymmetry between performing a computation to opposite directions. Given some big chungus integer such as 4922235242952026704037113243122008064, but not the formula that originally produced it, it is not quite easy to tell whether that integer is a perfect power, or some perfect power plus minus one.

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

Invalid hot key. Each hot key should be unique and valid
Hot keys:
CheckiO Extensions

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.

Pair Programming (Beta-version)

Welcome to Pair Programming! Engage in real-time collaboration on coding projects by starting a session and sharing the provided unique URL with friends or colleagues. This feature is perfect for joint project development, debugging, or learning new skills together. Simply click 'Start Session' to begin your collaborative coding journey!

Waiting for Pair Programming to start...

You are trying to join a pair programming session that has not started yet.

Please wait for the session creator to join.

Waiting for Pair Programming to reconnect...

It looks like the creator of the pair programming session closed the editor window.

It might happen accidentally, so that you can wait for reconnection.

<< <
> >>
exec show

Whats Next?

Free accounts will see Best CheckiO solutions with some delay.
Best Solutions will be opened in a moment
Become Awesome and Don't wait
The next stage is ""
Will be activated in
View More Solutions Random Review Solutions Go to the next mission