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Math problem in grade three! Urgent!
If a natural number can be expressed as the square difference of two natural numbers, it is called "wisdom number", for example, 16 = 52-32, 16 is a "wisdom number".

We must first find the distribution law of wisdom numbers.

Because 2k+ 1 = (k+ 1) 2-k 2,

Obviously, every number greater than 4 and multiples of 4 is also a wise number.

So the even number of 2 divided by 4 is not a wise number.

Therefore, the smallest wisdom number in the natural sequence is 3, and the second wisdom number is 5, starting from 5, followed by 5, 7 and 8; 9, 1 1, 12; 13, 15, 16; 17, 19, 20 ... that is, two odd numbers and multiples of 4 are arranged in groups of three.

3=2^2- 1^2,5=3^2-2^2,7=4^2-3^2,

8=3^2- 1^2,9=5^2-4^2,

1 1=6^2-5^2,……

This is a difficult problem to solve by arithmetic, and it is very simple to solve by algebra.

Let k be a natural number,

∵(k+ 1)^2-k^2=(k+ 1+k)(k+ 1-k)=2k+ 1,

Except 1, all odd numbers are "wisdom numbers".

And: (k+ 1) 2-(k- 1) 2.

=(k+ 1+k- 1)(k+ 1-k+ 1)= 4k,

All even numbers divisible by 4 are "wisdom numbers".

……

If we continue to explore, the problem will be clearer. Natural numbers starting from 1 are divided into four groups. Except for the 1 group, there are three "smart numbers", and the second one in each group is not a "smart number".