Skip to main content
OlympiadHQ

Browse · MathNet

Print

Estonian Math Competitions

Estonia number theory

Problem

Juku claims that if the sum of the squares of all digits of a natural number is divisible by then the number itself is divisible by . Is Juku's claim always true?
Solution
The sum of the squares of the digits of the number is which is divisible by , while the number is not divisible by .

Techniques

Modular ArithmeticDivisibility / Factorization