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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 225
Location: HKUST Math
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Posted: Fri Feb 06, 2004 11:08 pm Post subject: Remainder
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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.
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Soarer
Frequent VisitorJoined: 18 Jan 2004Posts: 181
Location: Hong Kong
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Posted: Fri Feb 06, 2004 11:23 pm Post subject:
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25*33*47-10
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Johnny Cheung
Joined: 25 Apr 2004Posts: 14
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Posted: Sun Apr 25, 2004 11:19 am Post subject: Re: Remainder
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Milton wrote:
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| 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.
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………….OBVIOUS ?!
YOU CAN ALSO USE thE 韓信點兵法的..
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beckham
Joined: 04 Jan 2005Posts: 2
Location: Hong Kong
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Posted: Tue Jan 04, 2005 7:05 pm Post subject: Re: Remainder
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Johnny Cheung wrote:
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Milton wrote:
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| 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.
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………….OBVIOUS ?!
YOU CAN ALSO USE thE 韓信點兵法的..
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What is 韓信點兵法 ???_________________
D.Beckham
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Andy
Frequent VisitorJoined: 28 Oct 2003Posts: 391
Location: Hong Kong
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Posted: Tue Jan 04, 2005 10:47 pm Post subject:
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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 Year-round.
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beckham
Joined: 04 Jan 2005Posts: 2
Location: Hong Kong
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Posted: Wed Jan 05, 2005 8:06 am Post subject:
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Andy wrote:
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| 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 .
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Thanks! I understand now._________________
D.Beckham
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