Brayden Chen, Ridgewood, USA

Integer Partition is a well known difficult problem in number theory and no solid solution has been found until today. The authors used Linear Difference Equation and Root of Unity to successfully get the expressions for integer n when the group number is k=2, k=3, k=4 and k=5. This proves the close relationship between integer partition and root of unity. With the analysis, it can be concluded that there will be an expression of U(n,k) existing for any n and k and we have found a method to develop the expression. Also this has provided a new interesting method to do further research in the integer partition area.

Integer Partition, Forward Difference Operator, Shift Operator, Linear Difference Equation, Root of Unity