# Log of arithmetic progression

Algebra Level 4

If $$x$$, $$y$$, $$z$$ and $$v$$ are 4 integers in an arithmetic progression and

$1000 ^ {\log (x)} + 1000 ^ {\log (y)} + 1000 ^ {\log (z)} = 1000 ^ {\log (v)}.$

Find the minimum possible value of $$x + y + z + v$$.

Clarification: All the logarithms are in base 10.

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