Arithmetic mean + interchange digits = geometric mean
Source: Bundeswettbewerb Mathematik 1972, round 2, problem 3
May 1, 2007
number theory proposednumber theory
Problem Statement
The arithmetic mean of two different positive integers is a two digit integer. If one interchanges the digits, the geometric mean of these numbers is archieved.
a) Find .
b) Show that a)'s solution is unique up to permutation if we work in base , but that there is no solution in base .
c) Give more numbers such that a) can be solved; give more of them such that a) can't be solved, too.