Never Ends in 2015

Number Theory Level 5

There are some 3-digit integers for which its multiples, never ends in 2015. We call these 3-digit numbers as \(N_{3}\)-numbers.

How many \(N_{3}\)-numbers are there?

For example:

\(100\times n\), where \(n\) is an integer, never ends in 2015; while for 131, we have \(131 \times 8565 = 1122015\), which ends in 2015.

This question is from the set starts, ends, never ends in 2015.


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