Euler's Lucky numbers are positive integers n such that m2 − m + n is a prime number for m = 0, …, n − 1.
How do we prove that if n is lucky, then n is prime?
Interesting post!
In my(poor) opinion to prove this we can't do what mr. melese offered...
Here is a link I think it be useful! Conjecture 17. The Ludovicus conjecture about the Euler trinomials
I spent half a day trying it many different ways. I attempted to prove this by contradiction at the beginning, but to prove being a composite is rather difficult because there isn't a mathematical expression for prime numbers, so I decided to prove it by contrapositive, but my main difficulty was here:
I let where and and .
Since , I let .
I ended up with , which led me to nowhere, and I decided to post the question.
I found your technique quite interesting. I see why you chose . It makes sense since . That's quite creative.