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.

# Currently Browsing

## August, 2012

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# Interval Scheduling Problem

11 August

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# Prime Congruence Class

Show that there are infinitely many primes of the form `4k - 1`

.

10 August

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# Sum of Divisors

Suppose we define the function as the sum of the divisors of n

Express in terms of ‘s prime factorization

9 August

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# That Other Little Gauss Story

Determine the product of distinct positive integer divisors of .

9 August

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# Congruence by L.C.M

Determine the number of **ordered pairs** of positive integers such that their least common multiple

9 August

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# Randomly Chosen Divisors

Compute the probability that a randomly chosen positive divisor of is an integer multiple of

9 August

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# Nothing in common

Let a and b be distinct integers such that . Show that

8 August

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# The Fib-Fib-Fib Sequence

Consider the sequences , defined recursively by

Show that

7 August

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# Square Sequence

The sequence satisfies

for all nonnegative integers n,m and . If , determine