MathDB

It is possible to perform three operations

f, g

, and

h

for positive integers:

f(n) = 10n, g(n) = 10n + 4

, and

h(2n) = n

; in other words, one may write

0

4

in the end of the number and one may divide an even number by

2

. Prove: every positive integer can be constructed starting from

4

and performing a finite number of the operations

f, g,

and

h

in some order.

Problem Statement