|
| Author |
Message |
|
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*47-10
|
|
|
|
|
|
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 Year-round.
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
All times are GMT + 8 Hours
|
|
| |
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
