#SAVE MY ASS AND I NEED TO SOLVE THE FACTORIAL EQUATION
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You can cancel n! on both sides.
(n - 5)!/(n - 3)! = (n-5)(n-6)(n-7)...1/(n - 3)(n - 4)(n - 5)... 1 so we can cancel the like terms and get 1/(n - 3)(n - 4).
42 = (n- 3)(n - 4).
Use quadratics and get the answer.
Or just, like, note that (n - 3) and (n - 4) are consecutive natural numbers.
Which multiply to 42.
That works too.
m(m + 1) = 42 where m is a natural number.