Finite field addition
Follow a modular line to its exact sum.
Every pale point satisfies y² = x³ + 7 modulo 97. P and Q determine a field line. Its third curve point becomes their sum after the y-coordinate is negated.
1. P
(5, 61)
2. Q
(29, 7)
3. P + Q
(62, 43)
Other exact constructions
(5, 61) + (29, 7) = (62, 43)
m = (yᵩ − yₚ) / (xᵩ − xₚ) = 22 mod 97
Blue residues satisfy the modular line through P and Q. C is its third curve point. Negating C's y-coordinate gives R = P + Q.
Field cursor (1, 28)