Topic Details (Notes format)

How to Calculate Modular Inverses

Subject: Mathematics

Book: Maths Mastery

A modular inverse of a number a (mod m) is x such that ax ≡ 1 (mod m). It exists only if gcd(a,m)=1. The Extended Euclidean Algorithm finds x for which ax + my=1, implying ax≡1 (mod m). For instance, to find the inverse of 3 modulo 7, we solve 3x + 7y=1, yielding x=5 because 3×5=15≡1 (mod 7). Modular inverses power encryption algorithms (RSA), solve congruences, and handle advanced computations in computer science. Mastery ensures you can manipulate modular arithmetic quickly for a wide range of cryptographic and number-theoretic tasks.

Practice Questions

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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