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

If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If two complementary angles differ by 30°, what are the angles?

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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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If a:b = 5:7 and b:c = 6:11, what is a:c?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If x^2 - 5x + 6 = 0, what are the roots?

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What is the greatest common divisor (GCD) of 36 and 48?

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If the radius of a circle is doubled, what happens to its area?

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