All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 A Composite Determination Problem (Posted on 2006-04-23)
Determine whether or not N is a composite number, where

N = 675*2621 + 677*2610 - 1

NOTE:
A prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. A composite number is a positive integer which has a positive divisor other than one or itself. By definition, every integer greater than one is either a prime number or a composite number. The numbers 0 and 1 are considered to be neither prime nor composite.

 See The Solution Submitted by K Sengupta Rating: 4.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 7 of 14 |
With a little excel help, I found out N is divisible by 29, and therefore composite.

675 mod 29 = 8
26^n mod 29 has a very long cycle, I believe of length 28
26^21 mod 29 = 12
677 mod 29 = 10
26^10 mod 29 = 5

8*12 + 10*5 - 1 = 9 + 21 - 1 = 0 mod 29

 Posted by Tristan on 2006-04-23 13:25:07

 Search: Search body:
Forums (0)