A question of primes (Posted on 2005-06-08)

	Submitted by pcbouhid
Rating: 2.8571 (7 votes)
Solution:	(Hide)
a) If n is odd, 14^n ends in 4. So does 11 x 14^n. Therefore, 11 x 14^n + 1 ends in 5, and hence is divisible by 5. b) If n is even, say equal to 2m, 11 x 14^n + 1 is equal to 11 x 196^m + 1. Since 196 = 3 x 65 + 1, (3 x 65 + 1)^m will always leave a remainder of 1 when divided by 3. Therefore, 11 x 196^m + 1 is equal to 11(3k + 1) + 1 = 33k + 12. Hence, when n is even, 11 x 14^n + 1 is always divisible by 3. Therefore, 11 x 14^n + 1 is never a prime, being a multiple of 5 or 3, according as n is odd or even.

	Subject	Author	Date
	Puzzle Solution	K Sengupta	2008-11-21 00:41:34
	Answer	K Sengupta	2008-11-07 01:27:45
	re(3): incomplete solu - thinking better	pcbouhid	2005-06-22 15:18:51
	re(2): incomplete solu - thinking better	Nick Hobson	2005-06-22 11:36:15
	re: incomplete solu - thinking better	pcbouhid	2005-06-22 03:26:54
	re: incomplete solu	pcbouhid	2005-06-21 16:55:39
	incomplete solu	phi	2005-06-21 09:11:13
	re: Trial and Error	pcbouhid	2005-06-11 23:23:27
	re: Trial and Error	Nick Hobson	2005-06-11 14:19:38
	Trial and Error	Paddy	2005-06-11 11:26:39
	Modulo solution	Nick Hobson	2005-06-09 12:30:05
	also	armando	2005-06-09 07:17:26
	full solution	Robby Goetschalckx	2005-06-08 14:00:19