2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225831For p=3 and for p=5 we prove that there are exactly p equivalence classes of p-coloured knots modulo (+/-1)--framed surgeries along unknots in the kernel of a p-colouring. These equivalence classes are represented by connect-sums of n left-hand (p,2)-torus knots with a given colouring when n=1,2,...,p. This gives a 3-colour and a 5-colour analogue of the surgery presentation of a knot.This is the version published by Algebraic & Geometric Topology on 24 May 2006Geometric Topology57M25, 57M10, 57M27text