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A Composite Determination Problem (Posted on 2006-04-23) Difficulty: 3 of 5
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)

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Solution Solution | Comment 1 of 14
N is composite.

26^21 is an even number.  Any number ending in 5 (such as 675) multiplied by an even number will end in 0.

677 ends in a 7, and any multiple of seven will end in either a 7, 9, 3, or 1.  I'm not sure which it will be in this case, but that's irrelevant.  All we need to know is that it will be odd.

So, we have a number ending in 0, plus a number ending in an odd digit, minus one.  This number N, whatever it might be, is obviously even and so must be composite.

  Posted by tomarken on 2006-04-23 10:54:04
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