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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 225
Location: HKUST Math

Posted: Fri Feb 06, 2004 11:08 pm Post subject: Remainder



X is the least positive integer such that (i) dividing X by 25 gives the remainder 15 (ii) dividing X by 33 gives the remainder 23 (iii) dividing X by 47 gives the remainder 37
Find X.





Soarer
Frequent VisitorJoined: 18 Jan 2004Posts: 181
Location: Hong Kong

Posted: Fri Feb 06, 2004 11:23 pm Post subject:



25*33*4710





Johnny Cheung
Joined: 25 Apr 2004Posts: 14

Posted: Sun Apr 25, 2004 11:19 am Post subject: Re: Remainder



Milton wrote:

X is the least positive integer such that (i) dividing X by 25 gives the remainder 15 (ii) dividing X by 33 gives the remainder 23 (iii) dividing X by 47 gives the remainder 37
Find X.

………….OBVIOUS ?!
YOU CAN ALSO USE thE 韓信點兵法的..





beckham
Joined: 04 Jan 2005Posts: 2
Location: Hong Kong

Posted: Tue Jan 04, 2005 7:05 pm Post subject: Re: Remainder



Johnny Cheung wrote:

Milton wrote:

X is the least positive integer such that (i) dividing X by 25 gives the remainder 15 (ii) dividing X by 33 gives the remainder 23 (iii) dividing X by 47 gives the remainder 37
Find X.

………….OBVIOUS ?!
YOU CAN ALSO USE thE 韓信點兵法的..

What is 韓信點兵法 ???_________________
D.Beckham





Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 391
Location: Hong Kong

Posted: Tue Jan 04, 2005 10:47 pm Post subject:



You need not apply Chinese Remainder Theorem (中國剩餘定理, that is 韓信點兵法 mentioned by Johnny Cheung).
As X + 10 is divisible by 25, 33 and 47, X + 10 is a commom multiple of 25, 33 and 47. Since their least common multiple (L.C.M.) is , the least possible value of X is .
_________________
Patience and tolerance are necessarily demanded Yearround.





beckham
Joined: 04 Jan 2005Posts: 2
Location: Hong Kong

Posted: Wed Jan 05, 2005 8:06 am Post subject:



Andy wrote:

You need not apply Chinese Remainder Theorem (中國剩餘定理, that is 韓信點兵法 mentioned by Johnny Cheung).
As X + 10 is divisible by 25, 33 and 47, X + 10 is a commom multiple of 25, 33 and 47. Since their least common multiple (L.C.M.) is , the least possible value of X is .

Thanks! I understand now._________________
D.Beckham





