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 JAMP  Vol.4 No.4 , April 2016
Non-Negative Integer Solutions of Two Diophantine Equations 2x + 9y = z2 and 5x + 9y = z2
Abstract: In this paper, we study two Diophantine equations of the type px + 9y = z2 , where p is a prime number. We find that the equation 2x + 9y = z2 has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, 3),(4, 1, 5)} but 5x + 9y = z2 has no non-negative integer solution.
Cite this paper: Khan, M. , Rashid, A. and Uddin, M. (2016) Non-Negative Integer Solutions of Two Diophantine Equations 2x + 9y = z2 and 5x + 9y = z2. Journal of Applied Mathematics and Physics, 4, 762-765. doi: 10.4236/jamp.2016.44086.
References

[1]   Sroysang, B. (2012) On the Diophantine Equation . International Journal of Pure and Applied Mathematics, 81, 605-608.

[2]   Sroysang, B. (2013) On the Diophantine Equation . International Journal of Pure and Applied Mathematics, 89, 111-114.

[3]   Sroysang, B. (2013) More on the Diophantine Equation . International Journal of Pure and Applied Mathematics, 84, 133-137.
http://dx.doi.org/10.12732/ijpam.v84i2.11

[4]   Rabago, J.F.T. (2013) On Two Diophantine Equations and . International Journal of Computing Science and Mathematics, 3, 28-29.

[5]   Acu, D. (2007) On a Diophantine Equation . General Math, 15, 145-148.

[6]   Chotchaisthit, S. (2012) On the Diophantine Equation Where p Is a Prime Number. American Journal of Mathematical and Management Sciences, 1, 191-193.

[7]   Mihailescu, P. (2004) Primary Cycolotomic Units and a Proof of Catalan’s Conjecture. Journal für die Reine und Angewandte Mathematik, 27, 167-195.

[8]   Suvarnamani, A. (2011) Solutions of the Diophantine Equation . International Journal of Mathematical Sciences and Applications, 1, 1415-1419.

[9]   Suvarnamani, A., Singta, A. and Chotchaisthit, S. (2011) On Two Diophantine Equations and . Science and Technology RMUTT Journal, 1, 25-28.

[10]   Rabago, J.F.T. (2013) More on the Diophantine Equation of Type . International Journal of Computing Science and Mathematics, 3, 15-16.

[11]   Sroysang, B. (2012) More on the Diophantine Equation . International Journal of Pure and Applied Mathematics, 81, 601-604.

[12]   Catalan, E. (1844) Note Extraite Dune Lettre Adressee a Lediteur. Journal für die Reine und Angewandte Mathematik, 27, 192.
http://dx.doi.org/10.1515/crll.1844.27.192

 
 
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