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- W2774080326 abstract "Let $pgeq 7$ be a prime, $lgeq 0$ be an integer and $k,~m$ be two positive integers, we obtain the following congruences, [ sumlimits_{s=lp}^{(l+1)p-1}binom{kp-1}{s}^mequivbegin{cases}binom{k-1}{l}^m2^{km(p-1)}pmod{p^3},&text{if}~2nmid m, binom{k-1}{l}^mbinom{kmp-2}{p-1}pmod{p^{4}},&text{if}~2mid m; end{cases} ] and [ sumlimits_{s=lp}^{(l+1)p-1}(-1)^sbinom{kp-1}{s}^mequivbegin{cases}(-1)^lbinom{k-1}{l}^m2^{km(p-1)}pmod{p^3}, &text{if}~2mid m, (-1)^lbinom{k-1}{l}^mbinom{kmp-2}{p-1}pmod{p^{4}}, &text{if}~2nmid m. end{cases} ] Let $p$ and $q$ are distinct odd primes and $k$ be a positive integer, we have [ binom{kpq-1}{(pq-1)/2}equiv binom{kp-1}{(p-1)/2}binom{kq-1}{(q-1)/2}pmod {pq}. ]" @default.
- W2774080326 created "2017-12-22" @default.
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- W2774080326 date "2018-06-01" @default.
- W2774080326 modified "2023-09-27" @default.
- W2774080326 title "A note on the congruences with sums of powers of binomial coefficients" @default.
- W2774080326 doi "https://doi.org/10.7169/facm/1694" @default.
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