MathDB

Vukasin, Dimitrije, Dusan, Stefan and Filip asked their teacher to guess three consecutive positive integers, after these true statements: Vukasin: " The sum of the digits of one number is prime number. The sum of the digits of another of the other two is, an even perfect number.(

n

is perfect if

\sigma\left(n\right)=2n

). The sum of the digits of the third number equals to the number of it's positive divisors". Dimitrije:"Everyone of those three numbers has at most two digits equal to

1

in their decimal representation". Dusan:"If we add

11

to exactly one of them, then we have a perfect square of an integer" Stefan:"Everyone of them has exactly one prime divisor less than

10

". Filip:"The three numbers are square free". Professor found the right answer. Which numbers did he mention?

Problem Statement