The authors calculate, modulo a prime, a long series for the six-particle contribution \(\tilde{\chi}^{(6)}\) to the magnetic susceptibility of the square lattice Ising model. This series has been used to obtain the Fuschian differential equation that annihilates \(\tilde{\chi}^{(6)}\).
The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime. The “depleted” differential operator is shown to have a structure similar to the corresponding operator for \(\tilde{\chi}^{(5)}\). The main result obtained by the authors on \(\tilde{\chi}^{(6)}\) are the order 3 and 4 operators which got in exact arithmetics.