Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Divisibility In Z & Euler Function
Let φ(n) be the cardinality of the set {a | 1 ≤ a ≤ n, (a, n) = 1} where (a, n) denotes the gcd of a and n. Which of the following is NOT true?
1
There exist infinitely many n such that φ(n) > φ(n + 1).
2
There exist infinitely many n such that φ(n) < φ(n + 1).
3
There exists N ∈ \(\mathbb{N}\) such that N > 2 and for all n > N, φ(N) < φ(n)
4
The set \(\left\{\frac{φ(n)}{n}: n ∈ \mathbb{N}\right\}\) has finitely many limit points.