Find the smallest integer n that makes 11 x 14^n + 1, a prime number, or, prove that it doesn't exist.

While Robby provided the general way for this problem type, in this case you can proceed like this:

155, 2157, 30185, 422577, 5916065, 82824897, ...

Odd terms finish in 5, so are multiple of 5; even terms finish always in 7: is there any rule for them? One of the first things to try is to sum the digits of each number. They are always multiple of 3. So even terms are  multiple of 3.

(To pcbouhid: I've take coffee at home today; you never know how will go on with suits...)

Edited on June 9, 2005, 7:46 am

Posted by armando on 2005-06-09 07:17:26