4

Part of 2018 Swedish Mathematical Competition

Problems(1)

1 among n consecutive pos. integers, is divisible by it's sum of digits

Source: 2018 Swedish Mathematical Competition p4

Find the least positive integer

n

with the property: Among arbitrarily

n

selected consecutive positive integers, all smaller than

2018

, there is at least one that is divisible by its sum of digits .

number theoryconsecutivesum of digitsdivisible