Product of Digits, ISI Entrance 2017

Product of Digits, ISI Entrance 2017

Understand the problem   Let (g : mathbb{N} to mathbb{N} ) with ( g(n) ) being the product of 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) ). Source of the problem...
Three Primes, ISI Subjective Entrance 2017

Three Primes, ISI Subjective Entrance 2017

Understand the problem Let (p_1,p_2,p_3)  be primes with (p_2neq p_3), such that (4+p_1p_2) and (4+p_1p_3) are perfect squares. Find all possible values of (p_1,p_2,p_3).    Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you really need a hint? Try it first!...