n^(k+4)-n^k=n^k(n^4- 1)=n^k(n^2+ 1)(n+ 1)(n- 1)

As long as the last bit of n(k+4)-n k is 0, it is obtained that the last bit of n (k+4) and n k are equal.

So as long as the last bit of a factor or the product of several factors of n k (n 2+1) (n+1) is 0.

Now discuss the value of n k (n 2+1) (n+1) (n-1):

n^k(n^2+ 1)(n+ 1)(n- 1)= n^(k- 1)[n(n^2+ 1)(n+ 1)(n- 1]

When the last bit of n is 0, the last bit of n is 0.

When the last digit of n is 1, the last digit of n- 1 is 0.

When the last digit of n is 2, the last digit of n (n 2+1) is 0.

When the last digit of n is 3, the last digit of n 2+1is 0.

When the last digit of n is 4, the last digit of n(n+ 1) is 0.

When the last digit of n is 5, the last digit of n(n+ 1) is 0.

When the last digit of n is 6, the last digit of n(n- 1) is 0.

When the last digit of n is 7, the last digit of n 2+1is 0.

When the last digit of n is 8, the last digit of n (n 2+1) is 0.

When the last digit of n is 9, the last digit of n+ 1 is 0.

The certificate is over.

Methods of learning mathematics well

1. Mathematics, like other disciplines, has many conceptual things. The basis of learning mathematics well is to understand what the definition is about.

For example, the meaning of square, cube and absolute value in mathematics.

We know that a square is the product of two identical numbers. Of course, a cube is the product of three identical numbers, and the absolute value is a value greater than or equal to 0. Knowing the true meaning of the definition, we took the first step and laid a solid foundation for the following study.

The difference between mathematics and other subjects is that there is no need to memorize, because mathematics does not test questions, but calculates, which is the biggest difference. How to practice specifically.

Many problems in mathematics are based on definitions. As I said before, once you understand the definition, it's easy to start. For example, if you want to merge similar items, you must first define them, that is, similar items. Simply put, it is something that everyone has. If you understand the definition, you will get twice the result with half the effort.