I get AC, but I can't undestand this...

var k,p,x,y:int64;
begin
k:=1;
p:=3;
x:=0;
y:=2;
// Like a test #0 (sample)
if (x*x+y*y)=k mod p then writeln('correct test') else writeln('uncorrect test');
// x^2+y^2=k(mod p)
end.

So, anybody can tell me, why sample test is "uncorrect"?

Because here can be many correct test, for example 0 1, 2 3 etc. So 1-st test is correct (0^2 + 2^2)mod 3 = 1(mod 3)

x^2+y^2 = k (mod p) mean in mathematics that (x^2 + y^2) mod p = k mod p