In how many ways can we pick three different numbers out of the group                                                   1,2,3,...,100   such that the largest number is larger than the product of the two smaller ones? (The order in which we pick the numbers does not matter.) Please answer without any computer programming or algorithms. Pure math only
In how many ways can we pick three different numbers out of the group $1,2,3,\dots,100$ such that the largest number is larger than the product of the two smaller ones? (The order in which we pick the numbers does not matter.)
This is what I have come up with so far, but I am rather lost at lines 3-4...  $$\begin{align} (a,b)\in A\times (B\setminus C)\iff&amp; a\in A \land b\in (B\setminus C)\\ \iff&amp; a\in A \land (b\in B \land \lnot(b\in C))\\ \iff&amp; (a\in A \land b\in B) \land (a\in A \land b\notin C)\\ \iff&amp; (a\in A \land b\in B)\setminus (a\in A \land b\in C)\\ \iff&amp; (a,b)\in (A\times B)\setminus ((a,b)\in A\times C)\\ \iff&amp; (a,b)\in (A\times B)\setminus (A\times C) \end{align}$$ How to split by commas that are not within parentheses? How to use the symbol \angle at the section title Shadow Incorrect at Bottom of Edge In the images below, I have a cube that is sticking up about two thirds through a plane. But, despite the fact that the cube is not hovering over the plane, the shadow seems to indicate otherwise. How can I fix this shadow? I've been told not to use for...in with arrays in JavaScript. Why not? I am trying to show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ coprime to $32760$. I have found the prime decomposition $32760 = 2^3 \cdot 3^3 \cdot 5 \cdot 7 \cdot 13$ and determined $\phi(32760)$, where $\phi$ is the Euler's totient function. This gives me that $\phi (32760) = 8640$.   Using Euler's congruence, this gives that $a^{8640} \equiv 1 \mod 32760$, but this is still far from the result I want to show... I also know a consequence of Eulers congruence, which states that $e \equiv e' \mod \phi (n)$ implies that $a^e \equiv a^{e'} \mod n$, but I do not see how to use this...  Any hints would be appreciated.  $\textbf{EDIT:}$ I made a mistake in my primefactorization, it is edited now. Number agreement between subject and object How are answers with the same vote score sorted? When a new question is asked how are the answers sorted?  I just answered a question and there were two other answers.  All three answers have 0 votes and no edits.  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