论文标题
Pythagorean Triples和JE $ \急性{S} $ Manowicz猜想的发电机
Generator of Pythagorean triples and Je$\acute{s}$manowicz conjecture
论文作者
论文摘要
令$ a，b，c $为相对质量的正整数，以便$ a^2+b^2 = c^2，2 | b $。在本文中，我们表明毕达哥拉斯$（a，b，c）$必须满足$ abc \ equiv {0 \; （\ mod3 \ cdot {4} \ cdot {5}}）$和$ c \ neq {0 \; （\ mod {3}}）$，我们还证明，对于$（a，b，c）\ in \ {（a，b，c）| （\ mod {5}}）\} \ bigCup \ {（a，b，c）| b \ equiv {0 \;（\ mod {12}}），c \ equiv {0 \ {0 \;（\ mod mod {5}}}}} $，是唯一的解决方案$$ a^x+b^y = c^z \ qquad {z}，y，z \ in {n} $$在正整数中为$（x，x，y，z）=（2，2，2,2）$。
Let $a,b,c$ be relatively prime positive integers such that $a^2+b^2=c^2, 2|b$. In this paper, we show that Pythagorean triples $(a, b,c)$ must satisfy $abc\equiv{0\; (\mod3\cdot{4}\cdot{5}})$ and $c\neq{0\; (\mod{3}})$, and we also prove that for $(a,b,c)\in\{(a,b,c)|a\equiv{0\;(\mod{3}}),b\equiv{0\;(\mod{4}}),c\equiv{0\; (\mod{5}})\}\bigcup\{(a,b,c)|b\equiv{0\;(\mod{12}}),c\equiv{0\;(\mod{5}})\}$, the only solution of $$a^x+b^y=c^z\qquad{z},y,z\in{N}$$ in positive integers is $(x, y, z) = (2, 2,2)$.
