On the exponential Diophantine equation $$(3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z$$(3pm2-1)x+(p(p-3)m2+1)y=(pm)z
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DOI: 10.1007/s10998-016-0162-z
Abstract: Let m be a positive integer, and let p be a prime with $$p \equiv 1~(\mathrm{mod}~4).$$p≡1(mod4). Then we show that the exponential Diophantine equation $$(3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z$$(3pm2-1)x+(p(p-3)m2+1)y=(pm)z has only the positive integer solution $$(x, y, z)=(1, 1,… read more here.
Keywords: 3pm 3pm2; exponential diophantine; diophantine equation; equation 3pm ... See more keywords