题目 Problem 614: Special partitions 2 An integer partition of a number n is a way of writing n as a sum of positive integers. Partitions …...

题目 Problem 618: Numbers with a given prime factor sum Consider the numbers 15, 16 and 18: 15 = 3×5 and 3+5 = 8. 16 = 2×2×2×2 and 2+2+2+2…...

题目 Problem 615. The millionth number with at least one million prime factors Consider the natural numbers having at least 5 prime factor…...

题目 Problem 617. Mirror Power Sequence For two integers n, e > 1, we define a(n,e)-MPS (Mirror Power Sequence) to be an infinite seque…...

题目 Problem 616: Creative numbers Alice plays the following game, she starts with a list of integers L and on each step she can either: …...

题目 Problem 613. Pythagorean Ant Dave is doing his homework on the balkony and, prepairing a presentation about Pythogorean triangles, ha…...

题目 Problem 612. Friend numbers Let's call two numbers friend numbers if their representation in base 10 has at least one common digi…...

题目 Problem 579. Lattice points in lattice cubes A lattice cube is a cube in which all vertices have integer coordinates. Let C(n) be the…...

题目 Prolem 610. Roman Numerals II A random generator produces a sequence of symbols drawn from the set {I, V, X, L, C, D, M, #}. Each ite…...

题目 Problem 89. Roman numerals For a number written in Roman numerals to be considered valid there are basic rules which must be followed…...

题目 Problem 609. π sequences For every n ≥ 1 the prime-counting function π(n) is equal to the number of primes not exceeding n. E.g. π(6)…...

题目 Problem 591: Best Approximations by Quadratic Integers Given a non-square integer d, any real x can be approximated arbitrarily close…...