MathDB

Finite n such that m+n|mn+1 - Iran NMO 2006 - Problem4

Source:

September 23, 2010

number theory proposednumber theory

Problem Statement

a.) Let

m>1

be a positive integer. Prove there exist finite number of positive integers

n

such that

m+n|mn+1

.
b.) For positive integers

m,n>2

, prove that there exists a sequence

a_0,a_1,\cdots,a_k

from positive integers greater than

2

that

a_0=m

a_k=n

and

a_i+a_{i+1}|a_ia_{i+1}+1

for

i=0,1,\cdots,k-1