2016 is absolutely awesome 18

Algebra Level 4

How many functions \(f:\mathbb{N}\rightarrow\mathbb{N}\) such that:

  • \(f(20160) = 1\)

  • for all \(x\) and \(y\), \(f(xy) = f(x)f(y)\)

  • for any \(n\) whose last digit is 3, \(f(n) = 1\).

Classification:

  • \(\mathbb{N}=\{0; 1; 2; 3; \ldots\}\)

This is a part of the Set.

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