MathDB

f(n) is product of sum of digits of n with n itself , f (n) = 19091997

Source: Dutch NMO 1997 p1

January 29, 2020

number theorysum of digitsProduct

Problem Statement

For each positive integer

n

we define

f (n)

as the product of the sum of the digits of

n

with

n

itself. Examples:

f (19) = (1 + 9) \times 19 = 190

f (97) = (9 + 7) \times 97 = 1552

. Show that there is no number

n

with

f (n) = 19091997