Modular arithmetic

There are 51 NRICH Mathematical resources connected to Modular arithmetic
Double time
problem

Double time

Age
16 to 18
Challenge level
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Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.
Grid lockout
problem

Grid lockout

Age
14 to 16
Challenge level
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What remainders do you get when square numbers are divided by 4?
The Public Key
problem

The public key

Age
16 to 18
Challenge level
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Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.
The Knapsack Problem and Public Key Cryptography
article

The knapsack problem and public key cryptography

An example of a simple Public Key code, called the Knapsack Code is described in this article, alongside some information on its origins. A knowledge of modular arithmetic is useful.
The Chinese Remainder Theorem
article

The chinese remainder theorem

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."
Small Groups
article

Small groups

Learn about the rules for a group and the different groups of 4 elements by doing some simple puzzles.