MathDB

g(n)= Product of digits of n

Source: ISI BStat - BMath Entrance Examination 2017, Problem 5

May 14, 2017

algebra

Problem Statement

Let

g:\mathbb{N} \to \mathbb{N}

with

g(n)

being the product of the digits of

n

.
(a) Prove that

g(n) \le n

for all

n\in \mathbb{N}

(b) Find all

n\in \mathbb{N}

for which

n^2-12n+36=g(n)