Considering the structural characteristics, the characteristic value is 1? ,5? ,7? To satisfy arithmetic progression, just take B = 5a and C = 7a, and put together similar Pythagorean numbers that all positive integers A can hold.

(2)

Proof: when one? ，bn？ ，cn？ Into arithmetic progression, then bn? Ann? =cn？ -bn？

Decomposition: (bn+an) (bn-an) = (cn+bn) (cn-bn)

Choose one about n, 4n(n? -1) do decomposition in two ways:

4n(n？ - 1)=(2n-2)(2n？ +2n)=(2n？ -2n)(2n+2) 4n(n？ - 1)

Compared with the target type, construct:

{an=n？ -2n+ 1

{bn=n？ +1 (n ≥ 4), the conclusion from the first question is that arithmetic progression is established.

{cn=n？ +2n- 1

By studying the relationship between the sides of a triangle, three sides of the triangle can be formed.

The following evidence is not similar to each other.

Any positive integer m, n, if △m and △n are similar, the three sides are proportional.

That is (m? -2m- 1)/(n？ -2n- 1)=(m？ + 1)/(n？ + 1)=(m？ +2m- 1)(n？ +2n- 1)

According to the nature of the proportion, it is (m-1)/(n-1) = (m+1) (n+1).

So m = n

Different values from the protocol are contradictory, so they are not similar to each other.