Journal of Jishou University(Natural Sciences Edition) ›› 2026, Vol. 47 ›› Issue (2): 6-9.DOI: 10.13438/j.cnki.jdzk.2026.02.002

• Mathematics • Previous Articles     Next Articles

Notations to Exponential Diophantine Equations (204m2+1)x+(237m2-1)y=(21m)z

WANG Cheng,YANG Hai,CHENG Yajie   

  1. (School of Science,Xi'an Polytechnic University,Xi'an 710048,China)
  • Online:2026-03-25 Published:2026-04-24

Abstract: Let m be a positive integer.By using the upper bound of solutions to the generalized Ramanujan-Nagell equation,Jacobi symbols,modular arithmetic,and methods of elementary number theory,it is proven that that the equation (204m2+1)x+(237m2-1)y=(21m)z only has the positive integer solution (x,y,z)=(1,1,2) when 2|/m,3|/m and m≡3,4(mod 7).

Key words: Jacobian symbol, positive integer solutions, Fibonacci numbers, Lucas numbers

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