Abstract—We prove a discrete analogue of the generalised entropypower inequality for log-concave randomvariables on the integers. As a special case, we showthat a conjecture of Tao (2010)holds true for log-concaverandomvariablesonthe integers:

H(X1+···+Xn+1)≥H(X1+···+Xn)+1 2 log n+1 n −o(1), where the o(1)-termvanishes asH(X1)→∞.

Explicit, finite bounds for theerror termareprovided,whichareexponential inH(X1). A full version of this paper is available at: arXiv:2210.06624.