Determine whether or not N is a composite number, where
N = 675*26^{21} + 677*26^{10}  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.
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 20060423 10:54:04 