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不定方程a^4±bc^4+am=ab的整数解

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 楼主| 发表于 2024-8-9 14:54 | 显示全部楼层
太阳 发表于 2024-8-9 00:02
已知:10ab2+a2b2=a3c2b=13+54ma=2bb5t
整数a0c0,\(m>0\ ...

太阳命题实实在在的太荒谬了——
已知:10ab^2+a^2*b^2=a^3*c^2,b=13+54m,a=2b,b≠5t
整数a≠0,c≠0,m>0,t>0,奇数b>0,素数p>0
求证:b=p

将a=2b带入原命题(方程)
20b^3+4b^4=8b^3*c^2
5+b=2c^2
b-2c^2+5=0

给定10000个连续b和520个连续c,共得115个整数解0,扣除b值中的5的倍数数,还有
以下92个b均满足太阳先生的所有条件,但其中超过一半的b(47个)不是素数——
b        分解式
67        67 is prime
283        283 is prime
877        877 is prime
1147        1147=31*37
2173        2173=41*53
3037        3037 is prime
3523        3523=13*271
4603        4603 is prime
5197        5197 is prime
6493        6493=43*151
8707        8707 is prime
9517        9517=31*307
12163        12163 is prime
14107        14107 is prime
15133        15133=37*409
17293        17293 is prime
18427        18427 is prime
20803        20803=71*293
24637        24637=71*347
25987        25987=13*1999
30253        30253 is prime
33277        33277=107*311
34843        34843 is prime
38083        38083 is prime
39757        39757=83*479
43213        43213=79*547
48667        48667=41*1187
50557        50557=13*3889
56443        56443 is prime
60547        60547=191*317
62653        62653 is prime
66973        66973 is prime
69187        69187=43*1609
73723        73723=13*53*107
80797        80797=43*1879
83227        83227 is prime
90733        90733=41*2213
95917        95917 is prime
98563        98563 is prime
103963        103963 is prime
106717        106717=13*8209
112333        112333=13*8641
121027        121027=37*3271
123997        123997 is prime
133123        133123=239*557
139387        139387 is prime
142573        142573 is prime
149053        149053 is prime
152347        152347=13*11719
159043        159043=89*1787
169357        169357=163*1039
172867        172867 is prime
183613        183613=31*5923
190957        190957=13*37*397
194683        194683 is prime
202243        202243 is prime
206077        206077 is prime
213853        213853=79*2707
225787        225787=41*5507
229837        229837 is prime
242203        242203=13*31*601
250627        250627=13*13*1483
254893        254893=37*83*83
263533        263533 is prime
267907        267907 is prime
276763        276763 is prime
290317        290317 is prime
294907        294907=79*3733
308893        308893=13*23761
318397        318397=191*1667
323203        323203=41*7883
332923        332923=67*4969
337837        337837 is prime
347773        347773 is prime
362947        362947=13*27919
368077        368077 is prime
383683        383683 is prime
394267        394267=43*53*173
399613        399613 is prime
410413        410413 is prime
415867        415867=197*2111
426883        426883=157*2719
443677        443677=13*34129
449347        449347 is prime
466573        466573 is prime
478237        478237=31*15427
484123        484123 is prime
496003        496003=563*881
501997        501997 is prime
514093        514093 is prime
532507        532507=439*1213
538717        538717=89*6053
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\frac{\square}{\square}\sqrt{\square}\square_{\baguet}^{\baguet}\overarc{\square}\ \dot{\baguet}\left(\square\right)\binom{\square}{\square}\begin{cases}\square\\\square\end{cases}\ \begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\to\Rightarrow\mapsto\alpha\ \theta\ \pi\times\div\pm\because\angle\ \infty
\frac{\square}{\square}\sqrt{\square}\sqrt[\baguet]{\square}\square_{\baguet}\square^{\baguet}\square_{\baguet}^{\baguet}\sum_{\baguet}^{\baguet}\prod_{\baguet}^{\baguet}\coprod_{\baguet}^{\baguet}\int_{\baguet}^{\baguet}\lim_{\baguet}\lim_{\baguet}^{\baguet}\bigcup_{\baguet}^{\baguet}\bigcap_{\baguet}^{\baguet}\bigwedge_{\baguet}^{\baguet}\bigvee_{\baguet}^{\baguet}
\underline{\square}\overline{\square}\overrightarrow{\square}\overleftarrow{\square}\overleftrightarrow{\square}\underrightarrow{\square}\underleftarrow{\square}\underleftrightarrow{\square}\dot{\baguet}\hat{\baguet}\vec{\baguet}\tilde{\baguet}
\left(\square\right)\left[\square\right]\left\{\square\right\}\left|\square\right|\left\langle\square\right\rangle\left\lVert\square\right\rVert\left\lfloor\square\right\rfloor\left\lceil\square\right\rceil\binom{\square}{\square}\boxed{\square}
\begin{cases}\square\\\square\end{cases}\begin{matrix}\square&\square\\\square&\square\end{matrix}\begin{pmatrix}\square&\square\\\square&\square\end{pmatrix}\begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\begin{Bmatrix}\square&\square\\\square&\square\end{Bmatrix}\begin{vmatrix}\square&\square\\\square&\square\end{vmatrix}\begin{Vmatrix}\square&\square\\\square&\square\end{Vmatrix}\begin{array}{l|l}\square&\square\\\hline\square&\square\end{array}
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\alpha\beta\gamma\Gamma\delta\Delta\epsilon\varepsilon\zeta\eta\theta\Theta\iota\kappa\varkappa\lambda\Lambda\mu\nu\xi\Xi\pi\Pi\varpi\rho\varrho\sigma\Sigma\tau\upsilon\Upsilon\phi\Phi\varphi\chi\psi\Psi\omega\Omega\digamma\vartheta\varsigma\mathbb{C}\mathbb{H}\mathbb{N}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{Z}\Re\Im\aleph\partial\nabla
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