A further exploration of the question of natural power and Modulus

In the last articleHttp://blog.csdn.net/acdreamers/article/details/38929067Learning to calculate the power of a natural number

And understand the elegant algorithms for finding bernuoli numbers. Today, let's look at two simple questions.

 

Problem:The sum of values.

 

Analysis:It is easy to see that the result of the continuous number is the same, that is, the cycle section length is. For, you need to first reduce the power, the formula used is as follows:

 

 

The worst time complexity is about.

 

 

Problem:Value. And is an odd number.

 

Analysis:First, let's focus on it. By

 

Here, because it is an odd number.

 

(1) If it is an odd number, it is offset. The answer is0.

(2) If it is an even number, then the remaining item is in the middle, that is, the answer is.

 

 

 

A further exploration of the question of natural power and Modulus