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    • 13 August
    Posted in Article, Math Problems
    0

    Linear Recursive Sequence

    We derive a general technique for solving full rank linear recursive sequences. Formally, a kth linear recursive sequence is defined as

        $$ x_n = a_1 x_{n-1} + a_2 x_{n-2} + a_3 x_{n-3} + \stackrel{k}{\ldots} + a_k x_{n-k} $$

    12 August
    Posted in Article, Math Problems
    0

    Odd Coprimes

    Let a be an odd integer. Prove that a^{2^n} + 2^{2^n} and a^{2^m}+2^{2^m} are relatively prime for all distinct positive integers n and m.

    12 August
    Posted in Article, Math Problems
    0

    More Prime Congruences

    Find all primes p and q such that p+q = (p-q)^3

    12 August
    Posted in Algorithm, Article, Lua
    1

    Interval Scheduling Problem

    Let’s consider the Interval Scheduling Problem, in which we have a set of n requests \{1,2,\cdots,n\}; the i^{th} request corresponds to an interval of time starting at s_i and finishing at f_i, or request $i$ spans interval $ [s_i,f_i]$. 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
    1

    Prime Congruence Class

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

    10 August
    Posted in Article, Math Problems
    0

    Just the Evens

    Find the sum of even positive divisors of 100000

    10 August
    Posted in Article, Math Problems
    1

    Sum of Divisors

    Suppose we define the function \sigma: \mathbb{N} \to \mathbb{N} as the sum of the divisors of n

        $$ \sigma(n) = \sum_{d|n} d $$

    Express \sigma(n) in terms of n‘s prime factorization

    9 August
    Posted in Article, Math Problems
    0

    That Other Little Gauss Story

    Determine the product of distinct positive integer divisors of n = 420^4.

    9 August
    Posted in Article, Math Problems
    0

    Congruence by L.C.M

    Determine the number of ordered pairs of positive integers (a,b) such that their least common multiple [a,b] = 2^35^711^{13}

    9 August
    Posted in Article, Math Problems
    0

    Randomly Chosen Divisors

    Compute the probability that a randomly chosen positive divisor of 10^{99} is an integer multiple of 10^{88}