# Elliptic curve division

If a generator point G is used to create a prime point and this generated point is then divided by any integer, the result gives a non-integer multiple of G.

Example: 2G / 4 = 0.5G

Does this point lie on the curve?

If it does not lie on the curve, what would be the most appropriate way to represent a point such as 0.5G on the elliptic curve graph?

Edit: Assume secp256k1 parameters.

• It depends on which kind of field the elliptic curve is defined. If finite field is used, there're only finite number of points in the curve and if the divisor is coprime with the number of points, we could transform the division into mulitplication. In other cases, the result could be not available or there could be multiple results Sep 4 '19 at 1:45
• Interesting. Assume we are using the secp256k1. I updated the question.
– user306666
Sep 4 '19 at 1:53

The curve is defined in a finite field $$F_p$$ and the number of points (order) in the ECC group is a big prime n. Cofactor of the ECC group to be 1 shows that all points in the curve could be generated by G.
To find X/m where m is coprime with n, we could first find the integer k so that $$mk=1(\mod n)$$ (Extend Euclidean algorithm could be used). After that we could replace X/m by kX.