# Does 2014 work?

Number Theory Level 4

A positive integer $$N$$ is divisible by 2014. Find the smallest possible value of the digit sum of $$N$$.

Details and assumptions

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is $$1 + 1 + 2 + 3 = 7$$.

×