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What are the Pythagorean numbers commonly used in mathematics?
Common Pythagorean numbers and several general formulas are:

( 1)

(3,

4,

5),

(6,

8, 10)

3n,4n,5n

(n is a positive integer)

(2)

(5, 12, 13)

,(

7,24,25),

(

9,40,4 1)

2n

+

1,

2n^2

+

2n,

2n^2

+

2n

+

1

(n is a positive integer)

(3)

(8, 15, 17),

( 12,35,37)

2^2*(n+ 1),[2(n+ 1)]^2- 1,[2(n+ 1)]^2+ 1

(n is a positive integer)

(4)m^2-n^2,2mn,m^2+n^2

(m and n are positive integers, m >;; n)

Simply list some:

three

four

five

five

12

13

seven

24

25

nine

40

4 1

1 1

60

6 1

13

84

Eighty-five

15

1 12

1 13

8, 15, 17

12,35,37

20,2 1,29

20,99, 10 1

48,55,73

60,9 1, 109