André Nicolas
Reputation
393/400 score
 8m comment How many phone number with $8$ digits exist s.t divide $2,3,5$ and there is no repetitive digit in it? @NNN: You are welcome. 25m answered How many phone number with $8$ digits exist s.t divide $2,3,5$ and there is no repetitive digit in it? 54m comment Show that the Hausdorff topology is unique in a finite set $X$ Let $x_0,x_1, \dots, x_n$ be the points. There is an open set $U_1$ that contains $x_0$ but not $x_1$. There is an open set that $U_2$ that contains $x_0$ but not $x_2$. And so on. The intersection of the $U_i$ is $\{x_0\}$. 2h comment How to prove that a very large number is not prime Looks like $10^{21}+1$, divisible by $11$. 4h answered Every morning the lecturer chooses pairs of students 4h comment Every morning the lecturer chooses pairs of students I think it is accessible. Just as a check on your calculations, $\Pr(X=3)=\frac{7}{12}$ (do this one first) and therefore $\Pr(X=1)=\frac{5}{12}$. 5h comment Every morning the lecturer chooses pairs of students If $X$ is the number of "mixed" pairs, then indeed the only possibilities are $X=1$ and $X=3$. Are you asked to find the distribution of the random variable $X$? 6h comment Find a close form expression for $f(x)$ Note that in general $(a_0+a_1x+a_2x^2+\cdots)(1+x+x^2+\cdots)=a_0+(a_0+a_1)x+(a_0+a_1+a_2)x^2+\cdots‌​$ 15h comment Find triples $(a,b,c)$ of positive integers such that… @almagest: I messed up on the wording. To reword, the smallest of $a,b,c$ is $\le 2$. So examine two cases, (i) smallest is $1$ and (ii) smallest is $2$. 16h answered Is a divides infinitely many repunits? 17h comment Incorporating input and output into Diophantine equations I do not understand the question, but there is no algorithm that will determine, given a Diophantine equation, whether that equation has a solution in the natural numbers (or integers). 17h comment Calculating the mean and variance of continuous distribution Your simulation seems to be a simulation of a discrete random variable. All your values are integers. 17h comment Calculating the mean and variance of continuous distribution What distribution should we assume? Not clear, but it seems reasonable to assume a continuous distribution. 17h comment Do monomials form a basis for the vector space of real analytic functions? Actually, they are I think clearly linearly independent but do not span. 18h answered If $p>5$ is prime, $2p+1$ is a prime, $\frac{4p+1}{3}$ is prime, $8p+1$ is prime, Then $p \equiv 29 (mod \; 30)$ 21h answered Show that the $C_n \geq 4^{n-1}/2^{n}$ where $C_n$ is the Catalan number 21h answered Use induction to prove that $2^n \gt n^3$ for every integer $n \ge 10$. 1d comment How to find sequence of digits in pi? It is not implausible that every finite sequence occurs, that is the case for "most" real numbers. 1d comment How to find sequence of digits in pi? It is not known whether every finite sequence of digits appears in the decimal expansion of $\pi$. The situation is no better for any base. 1d comment Exhibit isomorphism between $F$ and $F'$ A start: If you decide what $\alpha$ should be mapped to, in terms of $\beta$, or vice-versa, the full mapping will be determined.