A generalization of Wolstenholme's harmonic series congruence

作者：Pan, Hao^*

来源：Rocky Mountain Journal of Mathematics, 2008, 38(4): 1263-1269.

DOI：10.1216/RMJ-2008-38-4-1263

• Wolstenholme's harmonic series congruence
• Lucas sequence

Let A, B be two nonzero integers. Define the Lucas sequences {u(n)}(n=0)(infinity) and {v(n)}(n=0)(infinity) by
u(0) = 0, u(1) = 1, u(n) = Aun-1 -Bun-2 for n >= 2
and
v(0) = 0, v(1) = A, v(n) = Av(n-1) - Bv(n-2) for n >= 2
For any n is an element of Z( ), let w(n) be the largest divisor of u(n) prime to u(1), u(2),...., u(n-1). We prove that for any n >= 5
Sigma(n-1)(j=1) v(j)/u(j) equivalent to n(2)-1 Delta/6 . u(n)/v(n) (mod w(n)(2)),
where Delta = A(2) - 4B.

• 出版日期2008
• 单位上海交通大学