📘 modular arithmetic

1. The problem involves a custom operation \( \oplus \) defined on numbers arranged in a circular clock-like diagram with numbers from 0 to 7. 2. Given examples are:

1. The problem is to solve the expression $289 \times 125 \mod 27$. 2. We use the modular arithmetic property: $ (a \times b) \mod m = [(a \mod m) \times (b \mod m)] \mod m $.

1. The problem is to construct a multiplication table modulo 5. 2. Modulo operation means we take the remainder when dividing by 5.

1. The problem is to construct an addition table modulo 9. 2. Modulo addition means adding two numbers and then taking the remainder when divided by 9.

1. The problem is to construct an addition table in modulo 4. 2. In modulo arithmetic, addition is performed and then the remainder when divided by the modulus is taken.

1. The problem states that a man counts his cowries, representing 1 for each 10 counted. 2. This means he is grouping cowries in sets of 10 and counting each set as 1.

1. **Problem Statement:** Simplify each number modulo the given modulus. 2. **Formula and Rules:** For any integer $a$ and modulus $m$, the modulo operation is defined as $a \bmod

1. The problem is to simplify the given modular expressions: (a) $-3 \bmod 4$

1. **Problem Statement:** Determine the day of the week for March 14, 1988, given that March 14, 2021 was a Sunday. 2. **Formula and Explanation:** We use modular arithmetic to fin

1. The problem requires performing modular arithmetic operations for each given expression. 2. Recall that $a \bmod m$ means finding the remainder when $a$ is divided by $m$.