0To find Pythagorean triplets, we can try with 2m,m^2-1, and m^2+1
Since (2m)^2+(m^2-1)^2=4m^2+m^4-2m^2+1=m^4+2m^2+1=(m^2+1)^2
Example-Find Pythagorean triplets whose one number is 6
Let us try with 2m=6, then m=6/2=3,m^2-1=3^2-1=9-1=8, m^2+1=3^2+1=10
So the numbers are 6,8 and 10.We can verify 10^2=100=6^2+8^2=36+64=100
So the triplets are 6,8 and 10
Example 2) one number is 14, If 2m=14, m=14/2=7,m^2-1=7^2-1=49-1=48 and m^2+1=7^2+1=49+1=50
Now let us verify 14,48 and 50,50^2=14^2+48^2,2500=196+2304=2500,
So the numbers are 14,48 and 50
