MathDB

Consider a sequence of non-negative integers g

_1,g_2,g_3,...

each consisting of three digits (numbers smaller than

100

are also written with three digits; the number

27

, for example, is written as

027

). Each number consists of the preceding by taking the product of the three digits that make up the preceding. The resulting sequence is of course dependent on the choice of

g_1

(e.g.

g_1 = 359

leads to

g_2= 135

g_3= 015

g_4 = 000

).Prove that independent of the choice of

g_1

: (a)

g_{n+1}\le g_n

(b)

g_{10}= 000

Problem Statement