A peaceful day for all,

i count the amount of number

with c=u²+v² with gcd (u, v)=1 and c < 2^n

or better all the combination with u²+v²<2^n and gcd (u,v)=1

i do not understand what the gcd (u, v)=1 makes with the result.

the gcd (u,v)=1 is important for the construction of primitiv pyth. triples

as far as i can see.

for example: limit = 2^5 = 32

u, v = 1, 2

= 2, 3

= 2, 5

= 3, 4

Besides for me is the pair (2,5)=(5,2)

For every combination of (u,v) i could construct a=u²-v², b=2uv and

c=u²+v²

m=a/c and n=b/c is a vector in the unit circle

But i did not get the relationship with 2pi

Any ideas ?

Greetings from the primes

Bernhard