MathDB

China TST 1998 division probelm

Source: China TST 1998, problem 6

May 22, 2005

inductionLaTeXnumber theory unsolvednumber theory

Problem Statement

For any

h = 2^{r}

(

r

is a non-negative integer), find all

k \in \mathbb{N}

which satisfy the following condition: There exists an odd natural number

m > 1

and

n \in \mathbb{N}

, such that

k \mid m^{h} - 1, m \mid n^{\frac{m^{h}-1}{k}} + 1