勾股数新公式

Treenewbee

cz1 发表于 2024-2-7 11:02
设 m>=3 , 则 欧拉函数 φ(m) 总是偶数，

设 φ(m)=2024 ，求 m= ?

m={2645,3039,3243,4052,4232,4324,5290,6078,6348,6486}

Treenewbee

cz1 发表于 2024-2-7 18:52
求：\(x= ?\)  \(x^3\) （立方数）的最后四位数字是 \(2024\) .

\[x=2500 k -1826, k \in N^{+}\]

蔡家雄

蔡氏完全循环节问题

若 \(2*10^n - 51\) 是素数，则 10 是这个素数的原根。

谢谢树新蜂老师提供100000以内的 n={2, 3, 4, 8, 11, 13, 17, 28, 56, 105, 231, 339, 643, 922, 1219, 1880, 2209, 4238, 4987, 14770, 56194, 67043, 96867}

蔡家雄

求：\(a^3+b^3+c^3+2abc=d^3\)

Treenewbee

0<a<b<c<=500:

{{3,4,10,11},{6,8,20,22},{6,32,41,49},{8,45,58,69},{9,12,30,33},{10,166,263,287},{12,16,40,44},{12,64,82,98},{14,233,348,385},{15,20,50,55},{15,41,251,253},{16,90,116,138},{18,20,37,45},{18,24,60,66},{18,96,123,147},{21,28,70,77},{24,32,80,88},{24,128,164,196},{24,135,174,207},{24,197,267,308},{25,173,421,437},{27,30,74,83},{27,36,90,99},{30,40,100,110},{30,160,205,245},{32,180,232,276},{33,44,110,121},{35,88,140,163},{36,40,74,90},{36,48,120,132},{36,192,246,294},{36,208,221,285},{39,52,130,143},{40,225,290,345},{41,99,111,149},{42,56,140,154},{42,147,428,443},{42,224,287,343},{45,60,150,165},{45,119,154,192},{48,64,160,176},{48,256,328,392},{48,270,348,414},{51,68,170,187},{54,60,111,135},{54,60,148,166},{54,72,180,198},{54,288,369,441},{56,315,406,483},{57,76,190,209},{59,72,304,315},{59,86,188,211},{60,80,200,220},{60,320,410,490},{63,84,210,231},{64,360,464,552},{65,130,307,332},{66,88,220,242},{66,352,451,539},{69,92,230,253},{69,126,287,314},{70,176,280,326},{71,145,359,385},{72,80,148,180},{72,96,240,264},{72,384,492,588},{72,416,442,570},{73,147,294,328},{75,100,250,275},{76,323,344,451},{78,104,260,286},{81,90,222,249},{81,108,270,297},{81,139,194,246},{81,157,185,249},{82,198,222,298},{83,99,213,245},{83,142,353,382},{84,112,280,308},{87,116,290,319},{90,100,185,225},{90,120,300,330},{90,238,308,384},{90,291,394,475},{93,124,310,341},{96,128,320,352},{99,132,330,363},{101,149,249,301},{102,136,340,374},{103,116,209,256},{105,140,350,385},{105,264,420,489},{108,120,222,270},{108,120,296,332},{108,144,360,396},{108,178,417,457},{109,315,444,532},{110,406,445,581},{111,148,370,407},{114,152,380,418},{117,156,390,429},{118,172,376,422},{120,160,400,440},{123,164,410,451},{123,297,333,447},{126,140,259,315},{126,168,420,462},{129,172,430,473},{132,176,440,484},{135,150,370,415},{135,180,450,495},{135,357,462,576},{138,184,460,506},{141,188,470,517},{143,182,357,418},{144,160,296,360},{144,192,480,528},{147,196,490,539},{150,200,500,550},{151,188,401,460},{162,180,333,405},{162,180,444,498},{162,278,388,492},{162,314,370,498},{164,396,444,596},{166,198,426,490},{180,200,370,450},{198,220,407,495},{202,298,498,602},{206,232,418,512},{208,386,485,637},{212,230,233,385},{216,240,444,540},{229,240,306,445},{234,260,481,585},{261,286,455,588},{270,433,435,658},{424,460,466,770}}

蔡家雄

任意指数，任意项，任意系数的高次不定方程，

除了 程中占，

我相信 Treenewbee 能够突破任意系数的不定方程！

蔡家雄

求：\(x^{33}+y^{51}+z^{69}=w^{87}\)

各指数除以3，两两互质，应该有解，，，，