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Although Julius Caesar could not have solved this equation, the solution is related to him:

$\quad 63XY-14VZ = 8$

What is the solution?

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I think the solution is

August

Reasoning

Caesar Augustus lived from 63 BC to 14 AD.
Notice that BC and AD are almost Caesar cipher shifts of XY and VZ (by four places) if only we didn't have that pesky W. It turns out however, that "W" wasn't part of the Classical Latin alphabet so, in Caesar's time, this is a legitimate encoding.
August, which is named after him, is the 8th month of the year, which is why I think this is the answer.

As others have also mentioned in the comments, the answer could also be

October (relating to Octavian) which used to be the 8th month.

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    $\begingroup$ I had in mind two possible reasonings for the number 8, the other being the meaning of rot13 bpgnivna $\endgroup$
    – Improve
    Aug 20 at 5:39
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    $\begingroup$ In Caesar's time, October was the eighth month. $\endgroup$ Aug 20 at 12:49
  • $\begingroup$ ah, yes, misread that. Comments deleted. $\endgroup$
    – ikegami
    Aug 21 at 17:05

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