Waste less time on Facebook — follow Brilliant.
×

Fun with factorials

Find all natural numbers \(n\) such that \(n! | a^n+1 \) for all \(0\) <\( a \le n! \) with natural number \(a\).

Note by Surya Prakash Bugatha
2 years, 4 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Ehh, \(2^n+1\) is less than \(n!\) for \(n<4\), so you got only 3 cases to check...

Sreejato Bhattacharya - 2 years, 4 months ago

Log in to reply

Hint: What happens when \( a = 0 \)?

Calvin Lin Staff - 2 years, 4 months ago

Log in to reply

Ooops!! Typo fixed

Surya Prakash Bugatha - 2 years, 4 months ago

Log in to reply

Hint: What happens when \( a = 1 \)? What happens when \( a = n \)?

Calvin Lin Staff - 2 years, 4 months ago

Log in to reply

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...