Powers from Products of Consecutive Terms in Arithmetic Progression
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چکیده
A celebrated theorem of Erdős and Selfridge [14] states that the product of consecutive positive integers is never a perfect power. A more recent and equally appealing result is one of Darmon and Merel [11] who proved an old conjecture of Dénes to the effect that there do not exist three consecutive nth powers in arithmetic progression, provided n 3. One common generalization of these problems is to ask whether it is possible to have a product of consecutive terms in arithmetic progression equal to a perfect power. In general, the answer to this question is ‘yes’, as the Diophantine equation
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تاریخ انتشار 2006