参考答案：证明：∵51⁵¹-1=(49+2)⁵¹=1
=C⁰₅₁·49⁵¹+C¹₅₁·49⁵⁰·2+C²₅₁·49⁴⁹·2²+…+C⁵⁰₅₁·49·2⁵⁰+C⁵¹₅₁·2⁵¹-1
=49P+2⁵¹-1(P∈N^*)．
又∵2⁵¹-1=(2³)¹⁷=1
=(7+1)¹⁷-1
=C⁰₁₇·7¹⁷+C¹₁₇·7¹⁶+C²₁₇·7¹⁵+…+C¹⁶₁₇·7+C¹⁷₁₇-1
=7Q(Q∈N^*)．