# Modulo arithmetic

The differences between the The arguments are not modified. If an operand has array or function type, array-to-pointer and function-to-pointer conversions are applied. For the binary operators except shiftsif the promoted operands have different types, additional set of implicit conversions is applied, known as usual arithmetic conversions with the goal to produce the common type also accessible via the std:: If, prior to any integral promotion, one operand is of enumeration type and the other operand is of a floating-point type or a different enumeration type, this behavior is deprecated.

If both operands are signed or both are unsigned, the operand with lesser conversion rank is converted to the operand with the greater integer conversion rank Otherwise, if the unsigned operand's conversion rank is greater or equal to the conversion rank of the signed operand, the signed operand is converted to the unsigned operand's type.

Otherwise, if the signed operand's type can represent all values of the unsigned operand, the unsigned operand is converted to the signed operand's type Otherwise, both operands are converted to the unsigned counterpart of the signed operand's type.

The conversion rank above increases in order bool, signed char, short, int, long, long long. The rank of any unsigned type is equal to the rank of the corresponding signed type. The rank of char is equal to the rank of signed char and unsigned char.

When signed integer arithmetic operation overflows the result does not fit in the result typethe behavior is undefined:For the built-in operator, expression must have arithmetic, unscoped enumeration, or pointer type.

Integral promotion is performed on the operand if it has integral or unscoped enumeration type and determines the type of the result. Read and learn for free about the following article: What is modular arithmetic? If you're seeing this message, it means we're having trouble loading external resources on our website. We would say this as A A A A modulo B B B B is equal to R R R R.

Where B B B B is referred to as the modulus.

## Modular Arithmetic, Fermat Theorem, Carmichael Numbers - Numericana

For example. With a modulus of 3 we make a clock with numbers 0, 1, 2. We start at 0 and go through 5 numbers in counter-clockwise sequence (5 is negative) 2, 1, 0, 2, 1. We ended up at 1 so − 5 mod 3 = 1 -5 \text{ mod } 3 = \bf{1} − 5 mod 3 = 1. Later bash (starting from version ) re-implemented most of the advanced features of ksh93 plus a couple of its own.

Currently bash is restricted to integer arithmetic, while ksh93 can do floating-point arithmetic as well. Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity, which is known as the modulus (which would be 12 in the case of hours on a clock, or 60 in the case of minutes or seconds on a clock).

Formally, modular arithmetic is the arithmetic of any nontrivial. Inconsistent mathematics is the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed.

Tools from formal logic are used to make sure any contradictions are contained and that the overall theories remain coherent. Inconsistent mathematics.

Arithmetic operators - feelthefish.com