$2014=2\cdot19\cdot 3$ $53n^{55}-57n^{53}+4n\equiv 53n-57n\equiv 0\pmod 2$ $53n^{55}-57n^{53}+4n\equiv 15(n^{19})^2\cdot n^{17}-0\cdot n^{53}+4n\equiv 15n^{17}+4n\equiv 19n\equiv 0\pmod {19}$ $53n^{55}-57n^{53}+4n\equiv 0\cdot n^{55}-4n^{53}+4n\equiv -4n+4n\equiv 0\pmod{ 53}$ etc