MathDB

37

Part of PEN P Problems

Problems(1)

P 37

Source:

5/25/2007
Let Sn={1,n,n2,n3,⋯ }S_{n}=\{1,n,n^{2},n^{3}, \cdots \}, where nn is an integer greater than 11. Find the smallest number k=k(n)k=k(n) such that there is a number which may be expressed as a sum of kk (possibly repeated) elements in SnS_{n} in more than one way. (Rearrangements are considered the same.)
Additive Number Theory