# André Nicolas

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 May10 answered Polynomial $P(a)=b,P(b)=c,P(c)=a$ May10 comment Proving that if $c = gcd(f,g)$ then $c = kf + mg$ and that $m,k$ are unique You probably mean that $m$ and $k$ are in $\mathbb{F}[x]$. They are not unique. May10 answered Probability question about distinguishable and non distinguishable objects May10 comment Compute the Centroid of a Semicircle without Calculus The long lost but now found Method of Archimedes gives a procedure, but it too is based fundamentally on limiting processes. May10 revised Compute the Centroid of a Semicircle without Calculus added 316 characters in body May10 answered Compute the Centroid of a Semicircle without Calculus May10 answered Solution of a Diophantine equation involving powers May10 answered Find the point on the graph of $y=e^{2x}$ at which the tangent line passes through the origin May10 reviewed Approve suggested edit on Find a ternary $4\times 39$ matrix satisfying the conditions below May10 comment How I can find the expected value of $G$? The distribution is close to geometric. Let $X$ be the number of games. If $k$ is odd, $\Pr(X=k)=0$. If $k\ge 2$ is even, $\Pr(X=k)=\frac{1}{2^{k/2}}$. Try to see why this is true. If by tomorrow you haven't seen it, send a message and I will add to the answer. May10 revised Evaluate $\int_0^{\pi \over 3} \sec x\tan x\sqrt {\sec x + 2} \, dx$ using a substitution of your choice added 23 characters in body May10 comment Evaluate $\int_0^{\pi \over 3} \sec x\tan x\sqrt {\sec x + 2} \, dx$ using a substitution of your choice @Assad: It is contained in my answer. We go directly to $du=\sec x\tan x\,dx$, and see that that is part of the expression we want to integrate (which is what motivated the substitution). So we replace $\sec x\tan x\,dx$ by $du$, replace $\sec x+2$ by $u$, and we are done. I was also recalling an earlier question I am pretty sure was from you (same style) in which substitution took a long time. Don't bother with this $\frac{dx}{du}$ stuff. May10 revised Evaluate $\int_0^{\pi \over 3} \sec x\tan x\sqrt {\sec x + 2} \, dx$ using a substitution of your choice added 139 characters in body May10 answered Evaluate $\int_0^{\pi \over 3} \sec x\tan x\sqrt {\sec x + 2} \, dx$ using a substitution of your choice May9 revised calculate the number of possible number of words typo fix, Remark was not at end. May9 comment Can one use complex numbers in probability? The characteristic function $E(e^{it X})$ is useful. May9 comment Probability question using PIE For $5$ people, we can do it by reasonably well organized counting. Don't need PIE. By the time we get to $7$, need more structure. But in case you want crude, A's suitcase goes to one of the other $4$. Say it goes to B. We will count possibilities, then multiply by $4$. So A's goes to B. Two possibilities (i) B's goes to A or (ii) to someone else. Counting the possibilities for (i) is easy. Also for (ii). B's can go to one of C, D, E. Say it is C, but then we will multiply by $3$. Almost done. May9 comment calculate the number of possible number of words I imagine you mean at most one hyphen. The cute little trick I used won't work. Until I think of another, have to sum a series. For $k\ge 2$, the number of words of length $k$ is $36^{k-1}(34+k)$. Can add up from $2$ to $63$, there is a reatively simple closed form, and add the $36$ one-symbol words. will need to be away, can do details if someone has not done it already. May9 comment Combinatorics/Probability - Multiple Groups Example Problem @user1527227: We can make a labelled funeral urn for each species, want to put $2$ in one urn, $1$ each in the others. If this urn image is helpful, OK. But to me it doesn't suggest new ways of counting. May9 revised calculate the number of possible number of words added 250 characters in body