Modulo 7 refers to a system of arithmetic for integers, where numbers wrap around after reaching 7. It is a form of modular arithmetic often used in number theory and cryptography.
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Modulo 7 means that two numbers are congruent if their difference is divisible by 7.
Calculating 'a mod 7' yields the remainder when a is divided by 7.
In modulo 7 arithmetic, the numbers cycle through 0 to 6.
The equation 'x ≡ y (mod 7)' implies x and y have the same remainder when divided by 7.
Addition, subtraction, and multiplication operations can be performed under modulo 7 rules.
Review Questions
What is the remainder of 23 when divided by 7?
If x ≡ y (mod 7), what does this imply about x and y?
How does addition work in modulo 7 arithmetic?
Related terms
Congruence Relation: A type of equivalence relation in modular arithmetic where two numbers are considered equivalent if they have the same remainder when divided by a specified modulus.
Modular Arithmetic: A system of arithmetic for integers where numbers reset or wrap around upon reaching a certain value called the modulus.
Remainder: The amount left over after division when one integer is divided by another.