On-line Calculator for Modeling

Modular arithmetic is different from remainder arithmetic. "Module" is the transliteration of "Mod", and modular operations are mostly used in programming. Mod means redundancy. Modular arithmetic is widely used in number theory and program design. From the discrimination of odd and even numbers to the discrimination of prime numbers, from modular exponentiation to the calculation of [[maximum common number]], from grandson problem to Caesar cryptography, it is full of modular arithmetic. Although there are some introductions to modular arithmetic in many textbooks of number theory, most of them are based on pure theory, and the application of modular arithmetic in programming involves little.

For example \( 11 \bmod 2 \)，the value is 1

The above modulo operations are mostly used for programming, and an example is given to illustrate the principle of modulo operations:

Turbo Pascal's interpretation of mod is this:

$$ A \bmod B=A- \lfloor \frac{A}{B} \rfloor * B $$

(\( \lfloor x \rfloor \) means divisible)

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