Stage: 3 Challenge Level: 
What is the remainder when $2^{164}$ is divided by 7?
Properties of numbers. Number theory. Factors and multiples. Multiplication & division. Divisibility. Generalising. Modulus arithmetic. Mathematical reasoning & proof. Patterned numbers. Addition & subtraction.
Published December 1997.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk