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Ben
I'm a 28-year-old male from Cincinnati, OH. I am currently a mathematics graduate student at the University of Cincinnati. I obtained my B.A. degree from Carson-Newman College in 2000 with majors in mathematics and political science. I obtained a J.D. degree from the University of Akron School of Law in 2004, and passed the Ohio Bar Exam the same year. This year I began graduate studies in the field of mathematical sciences. I hope to earn a Ph.D. in mathematics, with a specialization in algebra. I am currently a Teaching Assistant at the University of Cincinnati for the course Topics in Mathematics.
For which real numbers k>0 is the function f:E^2->R given by f(x,y)=(x^2+y^2)^k differentiable?
Advanced Calculus Problem
2 AnswersMathematics1 decade agoFor any fixed positive integer d, prove the equation x^2-d*y^2=1 has infinite integer solutions.?
The original question is to prove that the group of units for the ring Z[sqrt(d)] is infinite when d>0. From my own work I have deduced that an element of Z[sqrt(d)] is a unit if and only if its components satisfy the equation x^2-d*y^2=(+/-)1. If it were real solutions, this would clearly be infinite, but I am stuck right now in trying to think of a way to prove that there are infinite solutions in integers.
1 AnswerMathematics1 decade ago