A Nice Factorial Equation | n!+(n-2)!=n^3+1 #maths

hi dear friends
here we have a very nice factorial equation: n!+(n-2)!=n^3+1
using properties of factorials and factoring the RHS, it is not hard to solve this problem
i hope you enjoy trying to deal with this question
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bye bye

[jureurh]

Hi ! It is possible that after step (n-2)!=n+1 we introduce new variable t=n-2, hence we get t!=t+3, t!-t=3,t((t-1)!-1)=3 and at and (t-1)!=(3/t)+1.Now it is obvius that 1<=t<=3.t can not be 2 only 1 or 3.At the end it is t=3 so n=5. 😀 Greetings from Slovenia