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# remainder

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28 May 2009, 08:09
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what is the remainder when 40! / 41? and when 39! / 41 ?
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28 May 2009, 11:28
40! mod 41 = 40 (any prime number - 1) mod prime number = prime number - 1
39! mod 41 = 1 (any prime number - 2) mod Prime number = 1

Proof to follow....
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AkamaiBrah
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28 May 2009, 11:31
Good to see you Akamai!
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GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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28 May 2009, 12:03
AkamaiBrah wrote:
40! mod 41 = 40 (any prime number - 1) mod prime number = prime number - 1
39! mod 41 = 1 (any prime number - 2) mod Prime number = 1

Proof to follow....

Actually, I don't think this is a fair GMAT question. The problem is an application of "Wilson's Theorem" which is far beyond the knowledge needed for the GMAT. I would be happy to see an answer that has a solution which falls under GMAT-required knowledge.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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30 May 2009, 23:50
40! =40! +1-1= (40! +1)+40-41

when 40! / 41 remainder is 40 since except 40 other terms are divisble by 41 and hence the remainder is 40/41 i.e. 40 .
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01 Jun 2009, 14:50
vcbabu wrote:
40! =40! +1-1= (40! +1)+40-41

when 40! / 41 remainder is 40 since except 40 other terms are divisble by 41 and hence the remainder is 40/41 i.e. 40 .

Hmmmm. Please demonstrate to me some proof or method to determine that (40! + 1) is divisible by 41. This is the same as saying 40! mod 41 = 40. Essentially, you are using the answer to the problem to find the answer -- circular logic.

If you are claiming that (n! + 1) is always divisible by n + 1, THAT IS WRONG; here is a simple counter example: (3! + 1) = 7 which is certainly NOT divisible by 4.

The ONLY time (n! + 1) is divisible by n + 1 is when n + 1 is PRIME, which is the essense of Wilson's formula and which no GMAT student should be expected to know.

Nuff said.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Re: remainder   [#permalink] 01 Jun 2009, 14:50
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