Solving An INSANELY Hard Viral Math Problem
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as the source of a power-sum problem when asking how the Newton-Girard identities apply, or whether a simpler method exists.
Recommended by 0 people across 0 different months, 2019 to 2021.
What it is
MindYourDecisions walks through a viral problem asking for x^4+y^4+z^4 given the sums of the first three powers. The video covers symmetric polynomials, power sum and elementary symmetric polynomials, and derives the Girard-Newton identities to get a general formula.
What people said
Cites ng.newbie · 2019-12 · Mathematics Stack Exchange · on “How is this power sum equation related to the Newton-Girard identity?”
I am trying to understand the logic behind solving this problem from youtube. [this video] Given the equation: $p_n-e_1p_{n-1}+\dots+n(-1)^ne_n = 0$ And the Newton-Girard identity: $ke_k = e_{k-1}p_1-e_{k-2}p_2+\dots+(-1)^{k-1}e_0p_k$ How are these 2 equations related ? Does it mean $ke_k = 0$ ? That makes no sense, yet looking at the right hand side of both the equations they both look the same. What is going on? I cant seem to understand.
Cites whatshappening · 2020-03 · Mathematics Stack Exchange · on “Calculate $x^4 + y^4 + z^4$ if $x + y + z = 1$ , $x^2 + y^2 + z^2 = 2$ and $x^3 + y^3 + z^3 = 3$”
I saw this problem here [this video] . Can anybody explain why I am getting different results using the following method. Notations: S(x 4 ) = sum of all terms (each having coefficient 1) consisting of only one variable to the power 4 = x 4 + y 4 + z 4 = A S(x 3 y) = sum of all terms (each having coefficient 1) consisting of 2 variables where one of them has power 3 and the other one has power 1 = x 3 y + x 3 z + y 3 x + y 3 z + …. = B Similarly, S(x 2 y 2 ) = C and S(x 2 yz) = D 1 4 = (x + y + z) 4 = S(x 4 ) + 4S(x 3 y) + 6S(x 2 y 2 ) + 12S(x 2 yz) [you can use this website to verify if you have doubt: [LINK] ] Or, 1 = A + 4B + 6C + 12D …………………………………….(1) 2 2 = (x 2 + y 2 + z 2 ) 2 = S(x 4 ) + 2
Cites Righter · 2021-04 · Mathematics Stack Exchange · on “Find sum of $5$th powers from given equations”
$$x+y+z=1 \ \ \ \ \ \ \ \ \ \ (1)$$ $$x^2+y^2+z^2=2\ \ \ \ \ \ \ \ \ \ (2)$$ $$x^3+y^3+z^3=3\ \ \ \ \ \ \ \ \ \ (3)$$ $$x^5+y^5+z^5=\ ?$$ I got this question from this YouTube video [this video] . The guy there, @Presh, explains a bunch of complicated stuff and gets the answer as $6$ . Is there a simpler method for this?