# Modulo Menu; Applications Of The Arithmetic Menu; Modular Arithmetic - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

Add two expressions modulo current modulus
DIVMOD
Divides 2 polynomials modulo current modulus
DIV2MOD
Euclidean division of 2 polynomials with modular
coefficients
EXPANDMOD Expands/simplify polynomial modulo current modulus
FACTORMOD Factorize a polynomial modulo current modulus
GCDMOD
GCD of 2 polynomials modulo current modulus
INVMOD
inverse of integer modulo current modulus
MOD
(not entry available in the help facility)
MODSTO
Changes modulo setting to specified value
MULTMOD
Multiplication of two polynomials modulo current modulus
POWMOD
Raises polynomial to a power modulo current modulus
SUBTMOD
Subtraction of 2 polynomials modulo current modulus

### Applications of the ARITHMETIC menu

This section is intended to present some of the background necessary for
application of the ARITHMETIC menu functions. Definitions are presented next
regarding the subjects of polynomials, polynomial fractions and modular
arithmetic. The examples presented below are presented independently of
the calculator setting (ALG or RPN)

### Modular arithmetic

Consider a counting system of integer numbers that periodically cycles back
on itself and starts again, such as the hours in a clock. Such counting system
is called a ring. Because the number of integers used in a ring is finite, the
arithmetic in this ring is called finite arithmetic. Let our system of finite integer
numbers consists of the numbers 0, 1, 2, 3, ..., n-1, n. We can also refer to
the arithmetic of this counting system as modular arithmetic of modulus n. In
the case of the hours of a clock, the modulus is 12. (If working with modular
arithmetic using the hours in a clock, however, we would have to use the
integer numbers 0, 1, 2, 3, ..., 10, 11, rather than 1, 2, 3,...,11, 12).
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