Required Mathematical Intelligence

Chapter 94 Inherited Numbers

A person's appearance can be inherited.Numbers can also be hereditary.

When doing squaring, numbers can also be inherited.For example:
52=25,

252 = 625.
In the above two equations:

5 and its square 25, the last digit is exactly the same (one inheritance);

25 and its square 625, the last two digits are exactly the same (two inheritance).

Is there any genetic phenomenon with more digits?The following series of equations provide examples of three-, four-, five-, and six-digit inheritance phenomena.

6252=390625,

06252=390625,

906252=8212890625,

8906252 = 793212890625.
[Answer: Strictly speaking, 0625 cannot be regarded as a four-digit number, but can only be regarded as a number on a four-digit combination lock.But its squaring does keep the four digits exactly at the end of the squared number.Moreover, counting 0625 in it also has the advantage of maintaining the continuity of evolution: the numbers on the left side of the above equations are 5, 25, 625, 0625, and 90625 in order of digits. , 890625.
This is a family with numerical inheritance under the square operation.From each number in this column of numbers, to get the adjacent number behind it, you only need to add an appropriate number in front of the original number; conversely, to get the adjacent number in front of a certain number in this column of numbers, you only need to Cross out the first digit of the original number.Just remember that one of the numbers in this column is 890625, and cross out its numbers one by one from front to back to get the first few numbers.

Here is another set of numbers with hereditary properties:
62=36,

762=5776,

3762=141376.]
(End of this chapter)