Answer:
(3,4,5)
(6,8,10)
(5,12,13)
(8,15,17)
(12,16,20)
(7,24,25)
(10,24,26)
(20,21,29)
(16,30,34)
(9,40,41)
Just choose 2 numbers from {1,2,3,4,5,6,7,8,...} and make sure the one you input for x is larger.
Post the three in the comments and I will check them for you.
Step-by-step explanation:
We need to choose 2 positive integers for x and y where x>y.
Positive integers are {1,2,3,4,5,6,7,.....}.
I'm going to start with (x,y)=(2,1).
x=2 and y=1.
So one Pythagorean Triple is (3,4,5).
I'm going to choose (x,y)=(3,1).
x=3 and y=1.
So another Pythagorean Triple is (6,8,10).
I'm going to choose (x,y)=(3,2).
x=3 and y=2.
So another is (5,12,13).
I'm going to choose (x,y)=(4,1).
Another is (8,15,17).
I'm going to choose (x,y)=(4,2).
We have another which is (12,16,20).
I'm going to choose (x,y)=(4,3).
We have another is (7,24,25).
You are just choosing numbers from the positive integer set {1,2,3,4,... } and making sure the number you plug in for x is higher than the number for y.
I will do one more.
Let's choose (x,y)=(5,1).
So (10,24,26) is another.
Let (x,y)=(5,2).
So another Pythagorean Triple is (20,21,29).
Choose (x,y)=(5,3).
Another Pythagorean Triple is (16,30,34).
Let (x,y)=(5,4)
Another is (9,40,41).