possibly. but "the number of shares" is not a specific enough concept. there are authorized shares, issued shares, outstanding shares, treasury shares, and probably other categories I can't think of right now. when the co buys back outstanding shares, they become treasury shares, and possibly the divisor in eps (ie, num of shares) stays fixed. but, the share price (and multiple of eps) might still go up because investors like dividends and share buybacks

corp fin is more complicated, and complex, and case-by-case, than can be fully covered or understood on a pilot forum. that's why teams of i bankers and securities lawyers work 2500 hrs a yr on the stuff

but to the OP, yes, eps has everything to do with our eventual ps deposit in March