本文選題：Jesmanowicz猜想 + 同余��； 參考：《西南大學(xué)》2015年碩士論文

【摘要】：本文利用簡(jiǎn)單同余、二次剩余、四次剩余及k次剩余特征理論,對(duì)關(guān)于不定方程(s2-t2)x(2st)y=(s2+t2)x的Jesmanowicz猜想的一些特殊情形進(jìn)行了證明,并得到如下結(jié)論：對(duì)于s-t=3的情形,t=n,且3|n,則當(dāng)下列條件之一成立時(shí),Jesmanowicz猜想成立.(I)n≠3(mod8)；(Ⅱ).n≡7(mod8),且2n+3具有模p≠1(modl6)的素因子(III)n≡9(mod16)；(IV)n≡4(mod16)；(V)n≡0(mod8),且2n+3不含4k+1形的素因子；(VI)n≡5(mod8),且2n+3不含4k+1形的素因子；(VII)n≡1(mod16),且2n+3不含4k+1形的素因子.對(duì)于s-t=5的情形,t=n,且5|n,則當(dāng)下列條件之一成立時(shí),Jesmanowicz猜想成立.(I)n≡2(mod8);(II)n≡6(mod8),且2n+5具有模p≠1(mod16)的素因子；(III)n≡4(mod16);(IV)n≡7(mod8).
[Abstract]:In this paper, by using the characteristic theories of simple congruence, quadratic residue, quartic residue and k-degree residue, we prove some special cases of Jesmanowicz's conjecture about the indefinite equation (s2-t2) x (2st) y = (s2t2) x. The following conclusions are obtained: for the case of s-t=3, then if one of the following conditions holds, then the conjecture is true. (I) n 鈮，

本文編號(hào)：2069986