Divisible by 2007 (Posted on 2007-03-11)

	Submitted by Dennis
Rating: 3.3333 (3 votes)
Solution:	(Hide)
Since (a-b) is a factor of (a^n - b^n), 446 is a factor of 3410^n - 2964^n. Also 1561 is a factor of 3000^n - 1439^n. But 446=2*223 and 1561=7*223 --> 223 is a factor of A. Similarly, 1971 is a factor of 3410^n - 1439^n and 36 is a factor of 3000^n - 2964^n. Since 36=4*9 and 1971=9*219, 9 is a factor of A. Now 9 and 223 are relatively prime --> 9*223=2007 is a factor of A.

	Subject	Author	Date
	Solution : With A Different Methodology	K Sengupta	2007-03-14 03:41:32
	re: Spoiler Ahead ! (public thank you with full solution)	ken	2007-03-11 14:07:25
	Spoiler Ahead !	K Sengupta	2007-03-11 11:36:50