Let’s consider the Interval Scheduling Problem, in which we have a set of n requests ; the request corresponds to an interval of time starting at and finishing at , or request spans interval . Suppose that a subset of the requests is compatible if no two of them overlap in time; find the largest compatible subset of any set of requests in a reasonable number of steps.
Show that there are infinitely many primes of the form
4k - 1.
Suppose we define the function as the sum of the divisors of n
Express in terms of ‘s prime factorization
Determine the product of distinct positive integer divisors of .
Determine the number of ordered pairs of positive integers such that their least common multiple
Compute the probability that a randomly chosen positive divisor of is an integer multiple of
Let a and b be distinct integers such that . Show that
Consider the sequences , defined recursively by