RE: Modular Arithmetic Problem?
- To: mathgroup at smc.vnet.net
- Subject: [mg38996] RE: [mg38975] Modular Arithmetic Problem?
- From: "Harvey P. Dale" <hpd1 at nyu.edu>
- Date: Fri, 24 Jan 2003 05:04:06 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
David: If n squared yields a five-digit answer, n must be 100 or greater but not more than 316. Only n's ending in 1 or 9 will produce a square ending in 1. Join[Range[101,316,10], Range[109,316,10]] generates all (43) such n's. It is simple to select from those the few (3) that yield 0 as the second digit in their squares: Select[<list>, IntegerDigits[#^2][[2]]== 0 &] They are: 101, 201, and 301. Given how few candidates there are to test (43), I wonder why this approach, even though it involves "testing a list of all possible candidate numbers," isn't the fastest and easiest route. Best, Harvey -----Original Message----- From: David Park [mailto:djmp at earthlink.net] To: mathgroup at smc.vnet.net Subject: [mg38996] [mg38975] Modular Arithmetic Problem? Dear MathGroup, Steven Shippee asked me about methods of solving the following problem. Find the numbers n such that n^2 is a five digit number with 0 in the second digit and 1 in the last digit. (i.e., x0xx1 where x is a digit 0..9). We know how to solve the problem by testing a list of all possible candidate numbers. But is there a method that uses Solve and modular arithimetic or some other clever method? If one looks at the answers one would think there must be. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/