Gonna party like it's 1999 (Posted on 2004-09-12)

	Submitted by SilverKnight
Rating: 3.2500 (4 votes)
Solution:	(Hide)
First note that: (2n)^4 = 16n^2 = 0 (mod 16) and (2n + 1)^4 = 16n^4 + 32n^3 + 24n^2 + 8n + 1 = 1 (mod 16) Therefore x4 = 0 or 1 (mod 16). This means that: a^4 + b^4 + . . . + n^4 (mod 16) is some number from 0 to 14, but 1999 = 15 (mod 16).

	Subject	Author	Date
	Puzzle Solution	K Sengupta	2022-06-20 22:01:23
	Logically Forced Solution	Michael	2004-11-26 21:01:03
	re(2): Solution	Richard	2004-09-12 18:49:04
	Observation	Charlie	2004-09-12 14:32:23
	re: Solution	David Shin	2004-09-12 13:51:53
	re: Answer	np_rt	2004-09-12 13:14:22
	Answer	Oskar	2004-09-12 10:48:50
	Solution	David Shin	2004-09-12 09:31:14