设p为素数,s,t∈N,a=sum form i=0 to ∞(aipi),r=sum form i=0 to ∞(ripi),这里ai,ri∈N,0≤ai≤p-1,0≤i≤t,0≤ri≤p-1,0≤i≤s,证明了Car≡Ca0r0…Casrs(mod p)和C(a+r)r≡C(a0+r0)r0C(a1+r1)r1…C(a1+r1)r1(mod p)两个同余式.据...设p为素数,s,t∈N,a=sum form i=0 to ∞(aipi),r=sum form i=0 to ∞(ripi),这里ai,ri∈N,0≤ai≤p-1,0≤i≤t,0≤ri≤p-1,0≤i≤s,证明了Car≡Ca0r0…Casrs(mod p)和C(a+r)r≡C(a0+r0)r0C(a1+r1)r1…C(a1+r1)r1(mod p)两个同余式.据此导出了杨辉三角的第a行以及第0行至第a行的二项系数中,使Car■0(mod p)的个数和使Car≡0(mod p)的个数,推出了斜列{C(a+r)r:r=0,1,…}中使C(a+r)r■0(mod p)的个数和使C(a+r)r≡0(mod p)的个数.展开更多
文摘设p为素数,s,t∈N,a=sum form i=0 to ∞(aipi),r=sum form i=0 to ∞(ripi),这里ai,ri∈N,0≤ai≤p-1,0≤i≤t,0≤ri≤p-1,0≤i≤s,证明了Car≡Ca0r0…Casrs(mod p)和C(a+r)r≡C(a0+r0)r0C(a1+r1)r1…C(a1+r1)r1(mod p)两个同余式.据此导出了杨辉三角的第a行以及第0行至第a行的二项系数中,使Car■0(mod p)的个数和使Car≡0(mod p)的个数,推出了斜列{C(a+r)r:r=0,1,…}中使C(a+r)r■0(mod p)的个数和使C(a+r)r≡0(mod p)的个数.
