We derive a general technique for solving full rank linear recursive sequences. Formally, a kth linear recursive sequence is defined as
We derive a general technique for solving full rank linear recursive sequences. Formally, a kth linear recursive sequence is defined as
Let a be an odd integer. Prove that and
are relatively prime for all distinct positive integers n and m.
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