Divisibility, Parity and the Division Algorithm
Divisibility, parity, and quotient-remainder division describe integer relationships used in computing. For integers $a$ and $b$, $a\mid b$ means $b=ak$ for some integer $k$.
Summary
Divisibility, parity, and quotient-remainder division describe integer relationships used in computing. For integers and , means for some integer . If and , then for any integers and .
🧠 Key Concepts
- Integer multiples
- Integer linear combinations
- Even integers
- Odd integers
- Parity invariants
- Unique quotient
- Nonnegative remainder
- Exact division
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Divisibility, Parity and the Division Algorithm
📘 Overview Divisibility identifies exact integer multiples, while parity classifies integers as even or odd. The division algorithm gives every integer a unique quotient and nonnegative remainder for a positive divisor, providing a foundation for modular arithmetic in computing.
🧠 Key Idea For any integer and positive integer , there are unique integers and
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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