BibTex RIS Kaynak Göster

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

Yıl 2014, Cilt: 2 Sayı: 2, 64 - 69, 01.12.2014

Öz

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

Kaynakça

  • 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: jicderivative@yahoo.com, jfrabago@gmail.com, jtrabago@upd.edu.ph
Yıl 2014, Cilt: 2 Sayı: 2, 64 - 69, 01.12.2014

Öz

Kaynakça

  • 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: jicderivative@yahoo.com, jfrabago@gmail.com, jtrabago@upd.edu.ph
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

JERICO B. Bacanı Bu kişi benim

Julius Fergyt. Rabago Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Gönderilme Tarihi 4 Nisan 2015
Yayımlandığı Sayı Yıl 2014 Cilt: 2 Sayı: 2

Kaynak Göster

APA Bacanı, J. B., & Rabago, J. F. (2014). ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2. Konuralp Journal of Mathematics, 2(2), 64-69.
AMA Bacanı JB, Rabago JF. ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2. Konuralp J. Math. Ekim 2014;2(2):64-69.
Chicago Bacanı, JERICO B., ve Julius Fergyt. Rabago. “ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2”. Konuralp Journal of Mathematics 2, sy. 2 (Ekim 2014): 64-69.
EndNote Bacanı JB, Rabago JF (01 Ekim 2014) ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2. Konuralp Journal of Mathematics 2 2 64–69.
IEEE J. B. Bacanı ve J. F. Rabago, “ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2”, Konuralp J. Math., c. 2, sy. 2, ss. 64–69, 2014.
ISNAD Bacanı, JERICO B. - Rabago, Julius Fergyt. “ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2”. Konuralp Journal of Mathematics 2/2 (Ekim 2014), 64-69.
JAMA Bacanı JB, Rabago JF. ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2. Konuralp J. Math. 2014;2:64–69.
MLA Bacanı, JERICO B. ve Julius Fergyt. Rabago. “ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2”. Konuralp Journal of Mathematics, c. 2, sy. 2, 2014, ss. 64-69.
Vancouver Bacanı JB, Rabago JF. ON THE DIOPHANTINE EQUATION 3^x + 5^y + 7^z = w^2. Konuralp J. Math. 2014;2(2):64-9.
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