MathDB

5

Part of 2017 ISI Entrance Examination

Problems(1)

g(n)= Product of digits of n

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

5/14/2017
Let g:N→Ng:\mathbb{N} \to \mathbb{N} with g(n)g(n) being the product of the digits of nn.
(a) Prove that g(n)≤ng(n) \le n for all n∈Nn\in \mathbb{N}
(b) Find all n∈Nn\in \mathbb{N} for which n2−12n+36=g(n)n^2-12n+36=g(n)
algebra