23 Oct 2013

IrMO 1998 P1 Q3: Cubes and Bases: Upper Secondary Mathematics Competition Question

Show that no integer of the form xyxy in base 10, where x and y are digits, can be the cube of an integer.

Find the smallest base b > 1 for which there is a perfect cube of the form xyxy in base b.


[Irish MO (IrMO) 1998 Paper 1 Question 3]


Feel free to comment, ask questions and even check your answer in the comments box below powered by  Disqus Google+.

}

This space is here to avoid seeing the answers before trying the problem!

}

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.
Related Posts Plugin for WordPress, Blogger...