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

then

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15 August

Posted in
Article, Math Problems

0

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

then

14 August

Posted in
Article, Math Problems

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

Define the sequence recursively by and

Find an explicit formula for in terms of n.

14 August

Posted in
Article, Math Problems

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

13 August

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Article, Math Problems

Find the general term of the sequence given by , and

13 August

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Article, Math Problems

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

13 August

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Article, Math Problems

We derive Binet’s equation for the n^{th} Fibonacci number as

13 August

Posted in
Article, Math Problems

We derive a general technique for solving full rank linear recursive sequences. Formally, a k^{th} linear recursive sequence is defined as

12 August

Posted in
Article, Math Problems

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