Topological invariance of integral Pontrjagin classes mod p

It is proved that integral Pontrjagin classes Pk mod p are topological invariant if p is odd, k < n(p) and they are not topological invariant if k ⩾ n(p), where n(p) is the smallest value of k for which p divides ek and ek is the smallest positive integer such that ekpk is topological invariant. For example, pk mod p is topological invariant for p = 3, 5, 11 etc. for every k ⩾ 1 but not topological invariant for p = 7 and k ⩾ 2.