Topic Details (Notes format)

Introduction to Euler’s Totient Function (φ)

Subject: Mathematics

Book: Maths Mastery

Euler’s Totient Function φ(n) counts how many integers ≤n are coprime to n. For prime p, φ(p)=p–1. For example, φ(8)=4 because only {1,3,5,7} are coprime with 8. This function is core in number theory and cryptography (Euler’s theorem, RSA encryption). Euler’s theorem states a^φ(n)≡1 (mod n) if gcd(a,n)=1. Understanding φ fosters advanced integer analysis, letting you compute exponents mod n or analyze prime-based structures. Mastery in totient calculations links to deeper insights in modern computer security and theoretical math.

Practice Questions

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

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What is the square root of 121?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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What is the sum of the first 50 positive integers?

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What is the sum of the interior angles of a hexagon?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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