DIVISIBILITY PROPERTIES OF INTEGERS x , k SATISFYING lk + ■ ■ ■ + ( x - i ) k = xk
نویسنده
چکیده
Based on congruences mod p and on properties of Bernoulli polynomials and Bernoulli numbers, several conditions are derived for x, k > 2 to satisfy the Diophantine equation 1k + 2k H-\(x 1 )* = xk . It is proved that ord2(x 3) = orà2k + 3 and that x cannot be divisible by any regular prime. Furthermore, by using the results of experiments with the above conditions on an SGI workstation it is proved that x cannot be divisible by any irregular prime < 10000 and that k is divisible by the least common multiple of all the integers < 200 .
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تاریخ انتشار 2010