Conclusion

Following completion of this free OpenLearn course, Introduction to number theory, as well as becoming proficient at modular arithmetic, you should find that you are increasingly able to communicate mathematical ideas and apply your knowledge and understanding to mathematics in everyday life, in particular to applications, such as the prevention of errors in ID numbers and in cryptography.

You should now be able to:

• find quotients and remainders from integer division
• apply Euclid’s algorithm and backwards substitution
• understand the definitions of congruences, residue classes and least residues
• add and subtract integers, modulo n, multiply integers and calculate powers, modulo n
• determine multiplicative inverses, modulo n and to use them to solve linear congruences.

This free OpenLearn course is an extract from the Open University module MST125 Essential mathematics 2. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] To see if you are ready to study MST125, click on the link and follow the ‘Am I ready?’ advice in the module description, and/or to refresh your knowledge of related mathematical topics consider MST124 Essential mathematics 1. If you are interested in statistics you may like to study the free OpenLearn course, Prices, location & spread, an adapted extract from the Open University module M140 Introducing statistics.