This is the 3743rd most frequent Russian word.
формуле
The word "формуле" is the dative or prepositional case of "формула," meaning "formula."
The word "формуле" is used here in the instrumental case to refer to the formula as a means or method of discussion.
Мы обсудили доказательство этой теоремы по данной формуле.
We discussed the proof of this theorem using the given formula.
The word "формуле" signifies locative relationship and use within the prepositional case here, meaning 'in' or 'by the formula'.
Ключ к решению задачи заключён в этой формуле.
The key to solving the problem is contained in this formula.
The word "формуле" is in the prepositional case indicating the topic of explanation being about or concerning the formula.