Yes. My method is as follows:
Let a be any odd number greater than 1, so a 2 is also an odd number, b=(a 2 -1)/2, c=(a 2 +1)/2,
=> (c-b)(c+b)=1*a2
=> a2+b2=c2
Since b+1=c, b and c are relatively prime.
a and b are also coprime, otherwise b and c are not coprime. a and c are the same.
Because a is (...), there are infinitely many sets of basic Pythagorean numbers.
Many years ago, the math teacher of the third grade wrote several groups of Pythagorean numbers on the blackboard, and then several groups of a, b, and c had this pattern (b+1=c). Mentioned it and asked if we had any rules.
The above does not contain (8,15,17) this group, another way:
Any a is an even number greater than 4 can contain it, but there will be cases where both b and c are even numbers.
The reason is that b=a 2 /4-1. a is even, a 2/4 may be odd.
Then set a=4k, where k is a positive integer.
Two odd numbers that differ by 2 are coprime. Others are the same as above.
over.