a + b + 3 \equiv 0 \pmod{9} \quad \Rightarrow \quad a + b \equiv 6 \pmod{9}

Fri, 01 May 2026 17:07:05 +0000

Understanding the Modular Equation: a + b + 3 ≡ 0 mod 9 ⇒ a + b ≡ 6 mod 9 Modular arithmetic is a powerful tool in number theory, widely used in cryptography, computer science, and solving problems in competitive mathematics. One common type of modular reasoning involves simple congruences, such as: a + b + 3 ≡ 0 mod 9 ⇒ a + b ≡ 6 mod 9 This equation highlights a fundamental transformation using properties of modular arithmetic, and understanding it unlocks deeper insight into solving modular problems efficiently.