ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2

Year 2014, Volume: 2 Issue: 2, 64 - 69, 01.12.2014

JERICO B. Bacanı Julius Fergyt. Rabago

https://izlik.org/JA84GD99KT

Abstract

We exhaust all solutions of the Diophantine equationx y+ 7z= win non-negative integers using elementary methods

Keywords

Exponential Diophantine equation , integer solutions

References

• D. Acu, On a Diophantine equation 2x+ 5y= z2, Gen. Math., 15, 2007, 145-148.
• S. Chotchaisthit, A. Singta, and A. Suvarnamani , On two Diophantine Equations 4x+7y= z2 and 4x+ 11y= z2, Sci. Technol. RMUTT J., 1, 2011, 25-28.
• S. Chotchaisthit, On a Diophantine equation 4x+ py= z2where p is a prime number, Amer. J. Math. Sci., 1 (2012), 191-193.
• S. Chotchaisthit, On a Diophantine equation 2x+ 11y= z2, Maejo Int. J. Sci. Technol., 7 (2013) 291-293.
• D. J. Leitner, Two exponential Diophantine equation, Journal de Th´eorie des Nombres de Bordeaux, 23 (2011), 479-487.
• P. Mih˘ailescu, Primary cycolotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math., 27 (2004), 167-195.
• A. D. Nicoar˘a and C. E. Pumnea, On a Diophantine equation of ax+ by= z2type, Educat¸ia Matematic˘a, 4 (2008), no. 1, 65-75.
• K. H. Rosen, Elementary Number Theory and its applications, fifth edition, Pearson Addison- Wesley, 2005.
• A. Rotkiewicz and W. Zlotkowski, On the Diophantine equation 1 + pα1+ · · · + pαk= y2, Colloq. Math. Soc. J´anos Bolyai, 51 (1990), 917937.
• R. Scott and R. Styer, On px− qy= c and related three term exponential Diophantine equations with prime bases, J. Number Theory, 105 (2004), 212-234.
• B. Sroysang, On the Diophantine equation 3x+5y= z2, Int. J. Pure Appl. Math., 81, (2012), 605-60
• B. Sroysang, On the Diophantine equation 8x+ 19y= z2, Int. J. Pure Appl. Math., 81, (2012), 601-604.
• B. Sroysang, On the Diophantine equation 31x+ 32y= z2, Int. J. Pure Appl. Math., 81, (2012), 609-612.
• B. Sroysang, On the Diophantine equation 7x+8y= z2, Int. J. Pure Appl. Math., 84, (2013), 111
• B. Sroysang, On the Diophantine equation 2x+3y= z2, Int. J. Pure Appl. Math., 84, (2013), No. 1, 133-137.
• B. Sroysang, On the Diophantine equation 5x+7y= z2, Int. J. Pure Appl. Math., 89, (2013), No. 1, 115-118.
• †Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio City 2600, PHILIPPINES ‡
• Institute of Mathematics, College of Science, University of the Philippines Dili- man, Quezon City 1101, PHILIPPINES E-mail address: [e-mail], [e-mail], [e-mail]