Some Congruence Properties of Binomial Coefficients
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چکیده
Using elementary methods, the following results are obtalned:(1) If p is n n-m prime, 0 m n, 0 < b < ap n-m, and p ab, then (m) (-I)P-I(apb (rood pn). 2 A2_4B If r,s are the roots of x Ax-B, where (A,B) and D > 0, if n n u v rn+s n, and k > O, then (II) v =v (rood pn). n r-s n kpn kpn-1 (III) If p is odd and p D, then u (_D) u (rood pn); kp n P kp n-I (IV) u (_1)Bu n) n n-I (rood 2 k2 k2
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