MathDB

The positive integer formed after writing

k

consecutive positive integers from smallest to largest is called a

k-\text{continuous}

number. For example

99100101

is a

3-\text{continuous}

number. Prove that: for

\forall N

k\in\mathbb Z^+

, there must be a

k-\text{continuous}

number that can be divisible by

N

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