What are some pythatgorean triples other than?

Question

3-4-5 , 5-2-13 , and 8-15-17?

Answer 1

7-24-25 , 33-56-65 to name a couple.

There is a general algorithm to find them:

take a and b to be positive integers, a < b.

Then (a^2 - b^2)^2 + (2ab)^2 = a^4 -2a^2b^2 + b^4 +4a^2b^2 = a^4 +2a^2b^2 + b^4 = (a^2 + b^2)^2

so [a^2 - b^2]-[2ab]-[a^2 + b^2] is always a pythagorean triple if a and b are integers, with a < b.

Answer 2

There are many. In fact, there are 16 where the third number is less than 100:

(3, 4, 5) (20, 21, 29) (11, 60, 61) (13, 84, 85)
(5, 12, 13) (12, 35, 37) (16, 63, 65) (36, 77, 85)
(8, 15, 17) (9, 40, 41) (33, 56, 65) (39, 80, 89)
(7, 24, 25) (28, 45, 53) (48, 55, 73) (65, 72, 97)

A simple recipe for generating more is at the link I provided.

Answer 3

Of course any multiple of these will be, such as 6-8-10, 9-12-15 etc, but I assume that is not what you want.

7-24-25
9-40-41
11-60-61
13-84-85
15-112-113
12-35-37
16-63-65
20-99-101
24-143-145
28-195-197

How's that for a start?

Answer 4

this method generally works


take and odd number and
square it and divide it by
2. Say 7, its square is 49
it can be split into two parts
24 and 25 , they form triplets

7-24-25,9(81)-40-41,11-60-61 etc.

Answer 5

U can compute them using
a=m^2+n^2; b=m^2-n^2; c=2mn where m and n are integers and m>n.