奥数难题,数论的,高手进答:∵f(x)/g(x) = q(x)+r(x)/g(x)在无穷多个正整数上取整值, 而q(x)总取整值,∴r(x)/g(x)在无穷多个正整数上取整值.若r(x)非零, 由其次数小于g(x), 对x充分大, 总有0 < |r(x)| < |g(x)|, 比值不为整数.至多只有有限个x使其为整数, 矛盾.∴r(x) = 0, g(x)...
数论奥数题答:即:18k+1,18k+2,18k+3,18k+4,18k+5,18k+6,18k+7,18k+8,18k+9,18k+10,18k+11,18k+12,18k+13,18k+14,18k+15,18k+16,18k+17,18k+18 对于任意2个数a=18k[1]+i[1]和b=18k[2]+i[2]a-b=18(k[1]-k[2])+(i[1]-i[2])若k[1]=k[2],根据mod(i,9)(i对9求余)...