Quote from: garlonicon on Today at 04:29:33 AM

How do you know that? Is there any simple way to check, if for a given p-value, there is such point or not?

the equation of the secp256k1 curve is
x³+7=y² mod(P)
or

x³+7-y²=0 mod(P)

if x=y
then
x³-x²+7=0

this equation is a polynomial of degree 3 in Finite Field and have no roots (solutions)

Quote

but there is one where x==y+1
Nice result! But how it was calculated?

instead of looking for x=y we can find if roots exists replacing x=y+c in the polynomial equation
where c in a constant varying between the range [-10;10] e.g
This is my Sage script:

Code:

P=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
C = EllipticCurve([F(0), F(7)])
F=GF(P)
R.<x>=F[]
for c in range(-10,10,1):
f=((x)**3+7)-(x+c)**2
rts=f.roots()
for r in rts:
try:
G=C.lift_x(r[0])
print(c,G,-G)
except:
pass

We test G and -G to see if one corresponding to x==y+c

Quote

Now I only wonder, what algorithm is needed to get there?

see above...