a primesieve of the kind f=1 or f=7 mod 8 with the function f(u,v)=u²+2uv-v²

[science_man_88]

Originally Posted by bhelmes

Example:
16²-15²+2*16*15 = 0 mod 511
20²-3² + 2*20*3 = 0 mod 511

Greetings from the metrics
Bernhard

Closest thing I see is that 2,3,5,17,23,31 don't divide it. Assuming it sums to the same number ( they do but 0 mod 511 is irrelevant).

[Batalov]

Originally Posted by bhelmes

u²-v²+2uv = 0 mod f and
r²-s²+2rs = 0 mod f (u,v,r,s element N, u<>r, v<>s, f=a*b)

can i calculate a factor of f ?

(u+v)^2 = 2v^2 mod f
(r+s)^2 = 2s^2 mod f

((u+v)/v)^2 = ((r+s)/s)^2 = 2 mod f

((u+v)/v)^2 - ((r+s)/s)^2 = 0 mod f

((u+v)/v - (r+s)/s) * ((u+v)/v + (r+s)/s) = 0 mod f

(u/v - r/s) * (u/v + r/s + 2) = 0 mod f

So, do gcd( u/v - r/s , f ) and gcd( u/v + r/s +2 , f ) (unless they are trivial) and see.

In your example:

? uv=Mod(16,511)/15
Mod(478, 511)
? rs=Mod(20,511)/3
Mod(177, 511)
? gcd(478-177, 511)
7
? gcd(478+177+2, 511)
73

[bhelmes]

A pleasant night for you, Batalov
and thanks a lot for this clear explication.