On the exponential Diophantine equation $ \left(\frac{q^{2l}-p^{2k}}{2}n\right)^x+(p^kq^ln)^y = \left(\frac{q^{2l}+p^{2k}}{2}n\right)^z $
Let $ k, l, m_1, m_2 $ be positive integers and let both $ p $ and $ q $ be odd primes such that $ p^k = 2^{m_1}-a^{m_2} $ and $ q^l = 2^{m_1}+a^{m_2} $ where $ a $ is odd prime with $ a\equiv 5\pmod 8 $ and $ a\not\equiv 1\pmod 5 $. In this paper, using only the elementary methods of factorization,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2022481?viewType=HTML |