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 the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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What is the area of an equilateral triangle with side length 10 cm?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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A car travels 240 km in 4 hours. What is its average speed?

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What is the square root of 121?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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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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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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