Some congruence properties of binomial coefficients and linear second order recurrences
[摘要] Using elementary methods, the following results are obtained:(I) Ifpis prime,0≤m≤n,0
0, ifun=rn−snr−s,vn=rn+sn, andk≥0, then (II)vkpn≡vkpn−1(modpn); (III) Ifpis odd andp∤D, thenukpn≡(Dp)ukpn−1(modpn); (IV)uk2n≡(−1)Buk2n−1(mod2n).
