For example, if we want the product of two numbers modulo n, then we multiply them normally and the answer is the remainder when the normal product is divided by n. The value n is …

Let m > 0 be a positive integer called the modulus. We say that two integers a and b. are congruent m. dulo m if b − a is divisible by m. In other words, �. dm) ⇐⇒ a − b = m · k for …

We have seen that modular arithmetic can both be easier than normal arithmetic (in how powers behave), and more difficult (in that we can’t always divide). But when n is a prime number, …

This is an example of when the modulus is 12 and for clocks we use f1, 2, ..., 12g instead of f0,1, ..., 11g, but these are the same because we consider 0 and 12 to be the same in terms of …

The modulus of elasticity (= Young’s modulus) E is a material property, that describes its stiffness and is therefore one of the most important properties of solid materials.

Modular arithmetic motivates many questions that don’t arise when study-ing classic arithmetic. For example, in classic arithmetic, adding a positive number a to another number b always …

Reduce each polynomial to a congruent polynomial of lowest possible degree with respect to the given modulus. For each pair of polynomials a(x); m(x) decide if there is an inverse modulo …