Problem If n is the numerator and d the denominator of a fraction, that fraction is defined a reduced fraction if and only if GCD(n,d)==1. For example $\displaystyle\frac{5}{16}$ is a reduced fraction, while $\displaystyle\frac{5}{16}$ is not, as both 6 and 16 are divisible by 2, thus the fraction can be reduced to $\displaystyle\frac{3}{8}$. Now, if you consider a given number d, how many reduced fractions can be built using d as a denominator?...
Problem Source: CSES Your task is to count for $k=1,2,…,n$ the number of ways two knights can be placed on a $k \times k$ chessboard so that they do not attack each other. For example: Input: 8 Output: 0 6 28 96 252 550 1056 1848 Solution Idea The most reachable method is for each of the first knight’s position, i’m looking for pertinent positions to place the second knight and sum them all....
Problem Source: Codewars The aim of the kata is to decompose $n!$(factorial n) into its prime factors. For example: Input: n = 12 Output: 2^10 * 3^5 * 5^2 * 7 * 11 Note that $n$ can reach 4000 and, of course, 4000! would be very big with more than 12000 digits ∑(O_O;) Solution Idea By definition, the factorial of a positive integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$: $$12!...