In this manuscript, the technique of evaluating all possible positive integer solutions to the Kaprekar number and an even perfect number of base 2 based on an equation l^?+m^?=?^? is enlightened.
Introduction
Conclusion
In this transmission, a method for obtaining positive integer solution to the equation? l?^?+m^?=?^? involving Kaprekar numbers is discovered. To conclude, one could look into another equation with different numbers.
References
Kaprekar, D.R. An interesting property of the number 6174. Scr. Math. 1955, 21, 304
Kaprekar, D., 1980. On Kaprekar Numbers. Journal of Recreational Mathematics, 13(2), 1980-81.
Hua.L.K, “Introduction to the Theory of Numbers”, Springer-Verlag, Berlin-New york, 1982.
Ivan Niven, Herbert, Zuckerman.S and Hugh Montgomery.L,“An Introduction to the theory of Numbers”, John Wiley and Sons Inc, New York 2004.
Gopalan.M.A, Vidhyalakshmi.S, Thiruniraiselvi.N and Kanaka.D, “On three special Generalized Fermat equations”, International Journal of Trend in Research and Development.2016; 3(1): 97-99.
Saranya. C and Janaki. G “On generalized fermat equations involving jarasandha numbers”, Parishodh Journal.2020; 9(2): 712-716.
Pandichelvi. V and Vanaja. R, “Novel approach of existence of solutions to the exponential equation ?(3m^2+3)?^x+(7m^2 )^y=z^2”, Turkish Journal of Computer and Mathematics Education,2021; 12(1): 376-381
Pandichelvi.V and Saranya.S, “Frustrating solutions for two exponential Diophantine equations ? p?^a+?(p+3)?^b-1=c^2 and (?p+1)?^a-p^b+1=c^2”, Journal of Xi’an Shiyou University, Natural Science Edition.2021; 17(5): 147-156.
Pandichelvi.V and Saranya.S,”Maddening solutions for an exponential Diophantine equation concerning definite prime numbers (2P+1)^u+(P-1)^v-2=w^2”, Advances and Applications in Mathematical Sciences.2022; 21(11): 6619-6625.
Pandichelvi.V and Vanaja.R, Inspecting integer solutions for an exponential Diophantine equation p^x+(p+2)^y=z^2, Advances and applications in mathematical sciences.2022; 21(8): 4693-4701.
Pandichelvi.V and Umamaheswari.B , “Exasperating non-negative integer solutions for an exponential diophantine equation (3u^2+5)p+(6u^2+11)=w^2”, 2022; 26(3): 1471-1475.
Pandichelvi.V and Umamaheswari.B “Perceiving solutions for an exponential diophantine equation linking Safe and Sophie germain primes q^x+p^y=z^2”. 2022; 52(2): 165-167.