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Summer 2003 REU Program |
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"Rational and Integer Points on Elliptic Curves"
Conducted by Aaron Bertram Dates: Monday, May 12 - Friday, June 20, 2003 Description: Consider the set of solutions (x,y) to the equation: y2 - x3 = -2 If we allow (x,y) to be real numbers, then such solutions are easy to find. They are: ((y2 + 2)1/3, y) and y can be any real number. But what if we want solutions that are rational numbers, or even integers? A little trial and error will show you that: (3,5) and (3,-5) are two such solutions. Are there any other integer solutions? (Hint: No.) Are there any other rational solutions? (Hint: Yes, lots.) We explored such questions in this REU and looked at how the rational points on elliptic curves can be used to produce fast algorithms for factoring large numbers, among other applications. Program Participants: Michael GiessingMajor: MathematicsJose Gonzalez |
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