On the Diophantine Equation Where is a Positive Integer
Keywords:
Diophantine equation , integer solution , non-negative integerAbstract
Background and Objectives : to find the solution to the Diophantine equation where and are non-negative integers, and is a positive integer, which is in the form for some non-negative integer .
Methodology : proving by contradiction and various properties related to the congruent in order to find the Diophantine equation’s solutions.
Main Results : the Diophantine equation has no any solution.
Conclusions : the Diophantine equation where is a positive integer, which is in the form for some non-negative integer , has no any solution for and are non-negative integers.
References
Asthana, S., & Singh, M. (2017). On the Diophantine Equation , International Journal of Pure and Applied Mathematics, 114(2), 301-304.
Burshtein, N. (2018). Solution of the Diophantine Equation when are Primes and . Annals of Pure and Applied Mathematics, 18(1), 101-106.
Chotchaisthit, S. (2012). On the Diophantine Equation where is a Prime Number. American Journal Mathematics and Science, 1(1), 191-193.
Kumar, S., Gupta, D., & Kishan, H. (2019). On the Solutions of Exponential Diophantine Equation . International Transactions in Mathematical Sciences and Computers, 11(1), 1-19.
Oliveria, N. (2018). On the Solvability of the Diophantine Equation when and are Primes, Annals of Pure and Applied Mathematics, 18(1), 9-13.
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