Có : M=1.(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)(2^{16}+1)
M=(2-1).(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)(2^{16}+1)
M=(2^{2}-1)(2^{2}+1)(2^{4}+1)(2^{8}+1)(2^{16}+1)
M=(2^{4}-1)(2^{4}+1)(2^{8}+1)(2^{16}+1)
M=(2^{8}-1)(2^{8}+1)(2^{16}+1)
M=(2^{16}-1)(2^{16}+1)
M=2^{32}-1 < 2^{32}-1 = N
=> M < N