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 …