# Currently Browsing

## August, 2012

12 August
Posted in Algorithm, Article, Lua

# Interval Scheduling Problem

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.

11 August
Posted in Article, Math Problems

# Prime Congruence Class

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

10 August
Posted in Article, Math Problems

# Just the Evens

Find the sum of even positive divisors of

10 August
Posted in Article, Math Problems

# 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
Posted in Article, Math Problems

# That Other Little Gauss Story

Determine the product of distinct positive integer divisors of .

9 August
Posted in Article, Math Problems

# Congruence by L.C.M

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

9 August
Posted in Article, Math Problems

# Randomly Chosen Divisors

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

9 August
Posted in Article, Math Problems

# Nothing in common

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

8 August
Posted in Article, Math Problems

# The Fib-Fib-Fib Sequence

Consider the sequences , defined recursively by

Show that

7 August
Posted in Article, Math Problems

# Square Sequence

The sequence satisfies

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