WebI was playing around with hypergeometric probabilities when I wound myself calculating the binomial coefficient $\binom{10}{3}$. I used the definition, and calculating in my head, I simplified to this expression before actually calculating anything $$ \frac {8\cdot9\cdot10}{2\cdot3} = 120 $$ And then it hit me that $8\cdot9\cdot10 = 6!$ and I … WebFeb 28, 2012 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
Determine all integral solutions of $a^2+b^2+c^2=a^2b^2$
WebMay 10, 2024 · (If this is true, any vector $(a,b,c)$ belonging to their span fulfills the same condition.) From this we get a system of three linear equations \begin{align*} 2c_1+c_2&=0\\ c_1-c_2+2c_3&=0\\ c_1+2c_2-2c_3&=0 \end{align*} Solving this system of equations we get that $(c_1,c_2,c_3)$ has to be a multiple of the vector $(2,4,3)$. WebIf a+ b+ c = 0 and a2 + b2 + c2 = ab +bc +ac, then it follows that 0 = (a+ b+ c)2 = a2 +b2 +c2 +2(ab+ bc +ac), or a2 +b2 +c2 = −2(ab +bc +ac). Put this together and we will see … gaskin company
$n = a^2 + b^2 = c^2 + d^2$. What are the properties of a, b, c …
WebOct 11, 2016 · Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange WebApr 19, 2024 · We have to somehow calculate (∑ a) % c in optimized manner. We can use divide and conquer to calculate it. The main idea is: If b is even then a*b = (2*a) * (b/2) If … WebNov 24, 2016 · Use the AM-GM inequality: 2 a 2 + 3 b 3 + 2 c 2 7 ≥ a 2 b 3 c 2 4 ⋅ 27 ⋅ 4 7 So we simplify: a 2 b 3 c 2 ≤ 432 ( 3 7) 7 = 944784 823543 ≃ 1.1472 Equality is attained (and that's important!) When all the terms are equal i.e. a 2 = b 3 = c 2. You can check this happens when a = 6 7, b = 9 7, c = 6 7. gaskin coat of arms