宮崎 隆史

研究内容

指数型不定方程式、ディオファントス解析

最近の研究業績

1. On the conjecture of Jesmanowicz concerning Pythagorean triples, Bull. Aust. Math. Soc. 80(2009), 413-422.

 

2. Exceptional cases of Terai's conjecture on Diophantine equations, Arch. Math. (Basel) 95(2010), 519-527.

 

3. Terai's conjecture on exponential Diophantine equations, Int. J. Number Theory 4(2011), 981-999.

 

4. The shuffle variant of Jesmanowicz' conjecture concerning Pythagorean triples, J. Aust. Math. Soc. 90(2011), 355-370.          

 

5. Jesmanowicz' conjecture on exponential Diophantine equations, Funct. Approx. Comment. Math. 45(2011), 207-229.         

 

6. The Diophantine equation (2am-1)^x+(2m)^y=(2am+1)^z, Int. J. Number Theory 8(2012), 2035-2044. (with Alain Togbe).

 

7. Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples, J. Number Theory 133(2013), 583-595. 

 

8. Jesmanowicz' conjecture with congruence relations, Colloq. Math. 128(2012), 211-222. (with Yasutsugu Fujita).

 

9. The shuffle variant of Terai's conjecture on exponential Diophantine equations, Publ. Math. Debrecen 83(2013), 43-62.  

 

10. Upper bounds for solutions of an exponential Diophantine equation, Rocky Mountain J. Math. 45(2015), 303-344.

 

11. On the exponential Diophantine equation (m^2+1)^x+(cm^2-1)^y=(am)^z, Bull. Aust. Math. Soc. 90(2014), 9-19. (with Nobuhiro Terai).

 

12. A note on the article by F. Luca ``On the system of Diophantine equations a^2+b^2=(m^2+1)^r and a^x+b^y=(m^2+1)^z'' (Acta Arith. 153 (2012), 373-392), Acta Arith. 164(2014), 31-42.

 

13. Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples II, J. Number Theory 141(2014), 184-201. (with Pingzhi Yuan and Danyao Wu).

 

14. Jesmanowicz' conjecture with congruence relations II, Canad. Math. Bull. 57(2014), 495-505. (with Yasutsugu Fujita).

 

15. On the Diophantine equation a^x+b^y=(a+2)^z, Acta Math. Hungar. 149(2016), 1-9. (with Alain Togbe and Pingzhi Yuan).

 

16. A remark on Jesmanowicz' conjecture for the non-coprimality case, Acta Math. Sinica, English Series. 31(2015), 1255-1260.

 

17. On the system of Diophantine equations (m^2-1)^r+b^2=c^2 and (m^2-1)^x+b^y=c^z, J. Number Theory 153(2015), 321-345. (with Florian Luca).

 

18. On Jesmanowicz' conjecture concerning primitive Pythagorean triples II, Acta Math. Hungar 147(2015), 286-293. (with Nobuhiro Terai).

 

19. On the equation 1^k+2^k+…+x^k=y^n for fixed x, J. Number Theory 163(2016), 43-60. (with Attila Berczes, Lajos Hajdu and Istvan Pink).

 

20. On the diophantine equation 1+x^a+z^b=y^n, accepted for publication. (with Attila Berczes, Lajos Hajdu and Istvan Pink).

居室

桐生キャンパス1号館4階1411号室