Recurrences and arithmetic

Concepts

• Recurrence relation 10 exercisesA recurrence relation is an equation that expresses each term a_n of a sequence in terms of the previous k terms; with initial va…
• Divisibility 10 exercisesAn integer a≠0 divides an integer b, written a| b, when b is an integer multiple of a.
• Greatest common divisor 10 exercisesThe greatest common divisor gcd(a,b) of two integers a and b, not both zero, is the largest integer that divides both.
• Euclidean algorithm 10 exercisesThe Euclidean algorithm computes the greatest common divisor of two integers a and b by dividing repeatedly, replacing each pair…
• Modular congruence 10 exercisesTwo integers a and b are congruent modulo a positive integer m if m divides their difference; equivalently, they leave the same r…
• Homogeneous linear recurrence 10 exercisesA homogeneous linear recurrence of order k expresses each term a_n as a combination of the previous k terms with constant coeffic…
• Prime number 10 exercisesA prime number p is an integer greater than 1 whose only positive divisors are 1 and itself.