Jul 23, 2025 · Given two integers L and R, denoting a range [L, R], the task is to find the smallest prime number present in the range. Examples: Input: L = 6, R = 11 Output: 7 Explanation: In …

For a natural number k, let p (k) denote the smallest prime number which does not divide k. If p (k) > 2, define q (k) to be the product of all primes less than p (k), otherwise let q (k) = 1.

6 days ago · OE Check the first few primes; 35 is not divisible by 2 or 3, but is divisible by 5, so 5 is the smallest prime factor of 35: !35! = 5. Now check the five choices: !10! = 2, and !15! , !45! …

Let p be an odd prime and let ζ be a primitive pth root of unity; that is, ζ is a complex number such that ζp = 1 and ζk 6= 1 for 1 ≤ k ≤ p − 1. Let Ap and Bp denote the set of quadratic residues …

Jan 22, 2022 · Lemma 1 11 2 If n> 1, there is a prime p such that p ∣ n. Proof Assume there is some integer n> 1 which has no prime divisor. Let S denote the set of all such integers. By the …

an = 4an 1 an 2 for n an odd pr 2015-A-5. Let q be an odd positive integer, and let Nq denote the number of integers a such that < a < q=4 and gcd(a; q) = 1. Show that Nq is odd if and only if q …

b) Find all positive integers smaller than 200 which leave remainder 1; 3; 4 upon division by 3; 5; 7 respectively.