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Abstract
We show that the Diophantine equation 2x+ 17y = z^2, has exactlyve solutions (x; y; z) in positive integers. The only solutions are (3; 1; 5), (5; 1; 7),(6; 1; 9), (7; 3; 71) and (9; 1; 23). This note, in turn, addresses an open problemproposed by Sroysang in [10].
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References
- Acu, D., On a Diophantine equation 2x + 5y = z2 , Gen. Math., 15:4 (2007), 145-148.
- Ivorra, W., Sur les ´equations xp + 2β yp = z2 et xp + 2β yp = 2z2 , Acta Arith., 108:4 (2003), 327-338.
- Mih˘ailescu, P., Primary cyclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math., 572 (2004), 167-195.
- Suvarnamani, A., Singta, A. and Chotchaisthit, S., On two Diophantine equations 4x + 7y =z2 and 4x + 11y = z2 , Sci. Technol. RMUTT J., 1 (2011), 25-28.
- Qi, L. and Li, X., The Diophantine equation 8x + py = z2 , Sci. World J., Vol. 2015, Article ID 306590, 3 pages.
- Rabago, J.F.T., On an open problem by B. Sroysang, Konuralp J. Math., 1:2 (2013), 30-32. [7] Rabago, J.F.T., A note on an open problem by B. Sroysang, Sci. Technol. RMUTT J., 3:1 (2013), 41-43.
- Sroysang, B., More on the Diophantine equation 8x + 19y = z2 , Int. J. Pure Appl. Math., 81:4 (2012), 601-604.
- Sroysang, B., On the Diophantine equation 31x + 32y = z2 , Int. J. Pure Appl. Math., 81:4 (2012), 609-612.
- Sroysang, B., More on Diophantine equation 2x + 19y = z2 , Int. J. Pure Appl. Math., 88:1 (2013), 157-160.
- Sroysang, B., More on the Diophantine equation 8x + 13y = z2 , Int. J. Pure Appl. Math., 90:1 (2014), 69-72.
- Yu, Y. and Li, X., The exponential Diophantine equation 2x + by = cz , Sci. World J., Vol. 2014, Article ID 401816, 3 pages
References
Acu, D., On a Diophantine equation 2x + 5y = z2 , Gen. Math., 15:4 (2007), 145-148.
Ivorra, W., Sur les ´equations xp + 2β yp = z2 et xp + 2β yp = 2z2 , Acta Arith., 108:4 (2003), 327-338.
Mih˘ailescu, P., Primary cyclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math., 572 (2004), 167-195.
Suvarnamani, A., Singta, A. and Chotchaisthit, S., On two Diophantine equations 4x + 7y =z2 and 4x + 11y = z2 , Sci. Technol. RMUTT J., 1 (2011), 25-28.
Qi, L. and Li, X., The Diophantine equation 8x + py = z2 , Sci. World J., Vol. 2015, Article ID 306590, 3 pages.
Rabago, J.F.T., On an open problem by B. Sroysang, Konuralp J. Math., 1:2 (2013), 30-32. [7] Rabago, J.F.T., A note on an open problem by B. Sroysang, Sci. Technol. RMUTT J., 3:1 (2013), 41-43.
Sroysang, B., More on the Diophantine equation 8x + 19y = z2 , Int. J. Pure Appl. Math., 81:4 (2012), 601-604.
Sroysang, B., On the Diophantine equation 31x + 32y = z2 , Int. J. Pure Appl. Math., 81:4 (2012), 609-612.
Sroysang, B., More on Diophantine equation 2x + 19y = z2 , Int. J. Pure Appl. Math., 88:1 (2013), 157-160.
Sroysang, B., More on the Diophantine equation 8x + 13y = z2 , Int. J. Pure Appl. Math., 90:1 (2014), 69-72.
Yu, Y. and Li, X., The exponential Diophantine equation 2x + by = cz , Sci. World J., Vol. 2014, Article ID 401816, 3 pages