# Currently Browsing

## August, 2012

15 August
Posted in Article, Math Problems

# Power Reduction in Congruences

Suppose you have integers a,b that are relatively prime to m such that

then

14 August
Posted in Article, Math Problems

# Even Pascals

Let , where k is an integer. Prove that for any positive integer n the number

is divisible by .

14 August
Posted in Article, Math Problems

# Sequences in Sequences

Define the sequence recursively by and

Find an explicit formula for in terms of n.

14 August
Posted in Article, Math Problems

# More Linear Recurrences

Let be defined by the recurrence relation , with . Show that the expression depends only on b and , but not on a.

13 August
Posted in Article, Math Problems

# Almost Linear

Find the general term of the sequence given by , and

13 August
Posted in Article, Math Problems

# Polynomial Divisors

Let . Show that for any positive integers there exists unique numbers such that the polynomial is divisible by p(x)

13 August
Posted in Article, Math Problems

# Analytical Fibonacci

We derive Binet’s equation for the nth Fibonacci number as

13 August
Posted in Article, Math Problems

# Linear Recursive Sequence

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

12 August
Posted in Article, Math Problems

# Odd Coprimes

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

12 August
Posted in Article, Math Problems

# More Prime Congruences

Find all primes p and q such that