[9up數學] 五次方程沒有解?

一般黎講 (ug or first year pg level) 都會assume A係commutative ring with unity or even pid

irreducibility同solvability by radicals係兩樣野黎
前者只係問係咪factorise到，有無root無關係
後者係問d roots係咪可以用radicals (using coefficients) 黎表達

C 係algebraically closed 所以有個更強的result係任何C[x] 的polynomials都可以factorised做product of linear factors in C[x], in particular, 任何大過degree 1的polynomial都reducible

我想知既係條algebra點用到落去，表面面積同體積係有用到，但同algebra有咩關係?

留名

一般嚟講好少會睇 A 唔係 commutative ring 以外嘅情況, 其中一個問題係 evaluation map A[X] -> A by f -> f(a) 唔係一個 homomorphism, 因為我地假設咗 ax = xa 係同一個 polynomial, 但如果我代 x=b, ab=ba 普遍嚟講唔會啱. 呢d情況 polynomial 嘅 factorisation 好麻煩

咁5次方程咪好適合用黎做密碼

copy paste textbook 都可以出po

關密碼咩事?

冇架啦
從來都係得一個variable先係得真解 (x+1 = 0, find x)
兩個都已經係 on9 (x+y = 10, find x y)

所有唔係新的知識都係copy and paste from somewhere

因為冇general solution, P唔等於NP

number theory 會討論diophantine equations

crypto 同coding已經out of my knowledge答唔到你

寫都寫好啲

其實連登唔係一個好地方

旨在帶下討論風氣啫，冇乜所謂嘅

我應該講左個key idea先然後再去討論個key idea點archieve到個目的

唔係無解，而係無一條只有四則運算同nth root的公式

例如quadratic equation個啲，姐係好似ax^2+bx+c=0, 咁同搵面積有咩關係?