# Good functions

Number Theory Level pending

Given an integer $$n\ge 2$$, a function $$f:\mathbb{Z}\rightarrow \{1,2,\ldots,n\}$$ is called good, if for any integer $$k,1\le k\le n-1$$ there exists an integer $$j(k)$$ such that for every integer $$m$$ we have $f(m+j(k))\equiv f(m+k)-f(m) \pmod{n+1}.$ Find the number of good functions when $$n=12$$.

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