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On the Diophantine Equation (m+1)^k(m^p -1) = m^q -1

Student-Run Applied & Math Seminar

Speaker: Roger Tian, UC Davis
Location: 2112 MSB
Start time: Wed, Oct 13 2010, 12:10PM

In this talk, we will analyze the exponential Diophantine equation (m+1)^k(m^p-1)=m^q-1 in the positive integers with m=>2 and explore certain methods for tackling it. In particular, we will solve this equation for the case that m is even. We will see that, interestingly, the above equation can be solved using elementary methods. Afterward, we will pose a conjecture related to the case that m is odd, and briefly discuss how this case might be tackled should the conjecture prove true.