Jeśmanowicz' conjecture with congruence relations

• Autorzy: Yasutsugu Fujita , Takafumi Miyazaki
• Języki publikacji: EN

Abstrakty

EN

Let a,b and c be relatively prime positive integers such that a²+b² = c². We prove that if $b ≡ 0 (mod 2^{r})$ and $b ≡ ±2^{r} (mod a)$ for some non-negative integer r, then the Diophantine equation $a^{x} + b^{y} = c^z$ has only the positive solution (x,y,z) = (2,2,2). We also show that the same holds if c ≡ -1 (mod a).

Kategorie tematyczne

• 11D61: Exponential equations
• 11D09: Quadratic and bilinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 2
• Strony: 211-222

Daty

wydano

2012

Twórcy

autor

Yasutsugu Fujita

• Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan

autor

Takafumi Miyazaki

• Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo, Japan

Identyfikatory

DOI

10.4064/cm128-2-6