The division of finite sums of powers of integers such as   n m i  i 1 2 ,   n m i  i   1 2 1 ,   n m i  i 1 3 ,   n m k  k 1 4 ,   n m k  k 1 5 has been developed by several authors in various books and articles. This thesis discusses the residual division of   n m i  i 1 7 by divisors 2, 3 …