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Limit Preserving Functions in CPOs

Very short proof that limit preserving functions (continuous functions) on complete partial orders are necessarily monotone.

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 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 