
Author 
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mmrproblem
Joined: 05 Nov 2004Posts: 16

Posted: Tue Jan 04, 2005 4:16 am Post subject: divisor



Find all n integer that can divisor 5n^(11)2n^(5)3n





Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 459
Location: Hong Kong

Posted: Tue Jan 04, 2005 3:53 pm Post subject:



Are you finding all integers n such that n divides ?
If so, all positive integers n satisfy your condition as .
_________________
Patience and tolerance are necessarily demanded Yearround.





mmrproblem
Joined: 05 Nov 2004Posts: 16

Posted: Thu Jan 06, 2005 3:26 am Post subject: divisor



My problem is:How many integer can be find that divisor of
5n^112n^53n for all positive integer value of n?





Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 459
Location: Hong Kong

Posted: Thu Jan 06, 2005 2:00 pm Post subject:



Are you going to find all positive integers k such that k divides for all positive integers n?_________________
Patience and tolerance are necessarily demanded Yearround.





mmrproblem
Joined: 05 Nov 2004Posts: 16

Posted: Fri Jan 07, 2005 6:26 am Post subject: divisor



exactly it is…





Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 459
Location: Hong Kong

Posted: Fri Jan 07, 2005 3:01 pm Post subject:



They are all factors of 90.
With the aid of modulo arithmetic, it is easy to check that is divisible by 2, 5 and 9 simultaneously, so the expression is divisible by and of course the factors of 90 as well for all positive integers n.
When n = 1 and 2, the expression equal and respectively. As 113 and 2459 are primes, the greatest common divisor of 10170 and 885240 is 90. It proves no other integer can satisfy the required property.
_________________
Patience and tolerance are necessarily demanded Yearround.





