自然数的等差分拆方法的改进

Improvement of partition with arithmetic progression of a natural numbers

讨论了自然数的等差分拆问题,结合自然数存在等差分拆时分拆的项数特点,分别给出了自然数s=pk,p为不小于3的奇数,k≥p+1/2;s=pk,p为不小于4的偶数,k≥p;s=pk,p为不小于2的自然数,k为奇数且k≥2p+1情况下的等差分拆的一般方法及方法数.

In this paper, the problem of equal difference splitting of natural numbers is discussed. Considering the characteristics of the item number of equal difference splitting of natural numbers, the natural numbers s=pk, p is not less than 3 odd numbers, k≥ p+1/2;s=pk , p is not less than 4 even numbers, k≥p;s=pk , p is not less than 2 natural numbers, k is odd numbers and k≥2p+1 . The general method and method number of equal difference splitting in the above case are given.