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 x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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

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The sum of the squares of two consecutive integers is 145. What are the integers?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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If the perimeter of a square is 40 cm, what is the area of the square?

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What is the square root of 121?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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