Centre for Advanced Studies in Mathematics

MATH PROBLEM OF
THE MONTH


Month	September - 2006

Problem	*Click here for Current Month Problem* Math Problem for September - 2006




Month	August - 2006

Problem	Math Problem for August - 2006

Solution	Solution

List of people with Correct Solution	Names will be uploaded soon.`



Month	July - 2006

Problem	Math Problem for July - 2006

Solution	Solution

List of people with Correct Solution	Lingli Sun (Institute of systems Science, Chinese Academy of Sciences, Beijing, China)



Month	June - 2006

Problem	Math Problem for June - 2006

Solution	Solution

	NO CORRECT SOLUTION RECEIVED



Month	May - 2006

Problem	Math Problem for May - 2006

Solution	Solution

List of people with Correct Solution	Pascal Buenzli (Ecole Polytechnique Federale de Lausanne (Switzerland) Ch. Bilal Saeed (Punjab University College of Information Technology (Lahore).



Month	April - 2006

Problem	Math Problem for April - 2006

	NO SOLUTION RECEIVED :: PROBLEM OPEN



Month	March - 2006

Problem	Math Problem for March - 2006

Solution	Solution

List of people with Correct Solution	Nabeel Butt (LUMS)



Month	February - 2006

Problem	Math Problem for February - 2006

Solution	Solution

List of people with Correct Solution	Nabeel Butt (LUMS)


Month	December - 2005

Problem	Math Problem for December-2005

Solution	Solution

List of people with Correct Solution	Wasiq Hussain (LUMS)


Month	November - 2005

Problem	Problem for November - 2005

Solution	Solution

List of people with Correct Solution	Nabeel Butt (LUMS) Nosheen Akram (LUMS)


Month	October - 2005

Problem	Math Problem for October-2005

Solution	Solution

List of people with Correct Solution	Iftekhar (The University of Western Ontario, Canada)


Month	September - 2005

Problem	Math Problem for September-2005

Solution	Solution

List of people with Correct Solution	Amer Iqbal (Washington University, USA) Nabeel (LUMS, Pakistan) Ch. Bilal Saeed (PUCIT, Lahore) Iftekhar (The University of Western Ontario, Canada)


Month	August - 2005

Problem	Math Problem for August2005

Solution	Solution

List of people with Correct Solution	Arif Zaman (LUMS, Pakistan) Nabeel (LUMS, Pakistan)


Month	July - 2005

Problem	Consider the equations. N = x³ (3x + 1) = y²(y + 1)³Where x, y are relatively prime positive integers. Show that there is only one possible value for N and find that value
Solution	Since (x,y) = 1 it follows that x³ divides (y + 1)³, hence x divides (y + 1) and x ≤ y +1. Similarly, y² divides (3x + 1) and so y²≤ 3x + 1. Combining the two inequalities gives, x²-5x = 0. As x is positive, only x = 1,2,3,4 and 5 are possible. Trying these values in x³(3x+1) = y²(y+1)³, we find that only x=5 and y=4 work. So, N = (4)²(5)³= 2000 is the only solution.
Remarks	This problem was intended to be an �appetizer� for students and faculty members alike. It was actually a derivative of the �Workshop of Computational Number Theory and Cryptography� organized by CASM. There were no tricks to the problem as can be observed from the solution above. However, I received several queries regarding the meaning of �relatively prime� in the question. As far as the solution is concerned, merely coming up with an answer of N = 2000 was not the only ingredient that I was looking for in a correct solution. In fact, a lot of credit went to the way in which the problem was approached. Since, it was the first online problem organized by CASM; this particular review process could be described as so called lenient.
List of people with Correct Solution	Nabeel Butt (LUMS, Pakistan) Wasiq Hussain (LUMS, Pakistan) Fethi Belgacem (Arab Open University, Kuwait)