Cubing the square (Posted on 2013-01-30)

	Submitted by broll
Rating: 5.0000 (1 votes)
Solution:	(Hide)
Excel can be used for the first part to derive 531441 by inspection, comparing the cubes mod 1000 with a list of squares mod 1000. Alternatively, using wolframalpha: x^6=441 mod 1000 when x == 9 || x == 241 || x == 259 || x == 491 || x == 509 || x == 741 || x == 759 || x == 991, giving 9^6, or 3^12 as the minimal solution. Then for the second part, start with the idea that (1000a+b)^n, where b is some number between 0 and 999 factors to:1000a(various factors)+b^n, with no change in the last 3 digits of b^n. x^7=441 mod 1000 gives x=721. Then x^6=721 mod 1000 gives {x == 121 || x == 129 || x == 371 || x == 379 || x == 621 || x == 629 || x == 871 || x == 879}. But if x^6 is 721 mod 1000 and x^(7*6) is 441 mod 1000, then x=121^42=11^84 is the minimal solution.

	Subject	Author	Date
	re(4): Programming and Excel	broll	2013-01-31 03:14:19
	re(3): Programming and Excel	brianjn	2013-01-31 02:14:31
	re(2): Programming and Excel	broll	2013-01-31 02:02:37
	re: Programming and Excel	brianjn	2013-01-30 17:51:17
	Programming and Excel	brianjn	2013-01-30 17:37:24
	computer solution	Charlie	2013-01-30 15:56:53
	found y, got bonus	Jer	2013-01-30 14:51:54
	x, not y but some thoughts	Jer	2013-01-30 14:33:57