Question

Construct the Cayley Table for

the group formed by the points on the curve y2=x3+2x+18
(mod 19)

Answer 1

The Cayley Table for the group formed by the given points on the curve can be constructed by performing the group operation on each pair of points.

Step-by-step explanation:

The Cayley Table for the group formed by the points on the curve y^2=x^3+2x+18 (mod 19) can be constructed by performing the group operation on each pair of points. The group operation is defined as adding two points on the curve and taking the modulo 19 of the resulting point. Here is the Cayley Table for the given points:

+(1,5)(2,10)(3,7)(4,14)(1,5)(2,10)(3,7)(4,14)(2,10)(3,7)(4,14)(1,5)(3,7)(4,14)(1,5)(2,10)(4,14)(1,5)(2,10)(3,7)