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Ewan Delanoy

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30
Interesting Olympiad Style Problem about Invariance
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26
Is it possible for an irreducible polynomial with rational coefficients to have three zeros in an arithmetic progression?
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25
Does there exist rational $a,b,c$, such that $\sqrt[3]{1}+\sqrt[3]{2}+\sqrt[3]{4}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$
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22
How to prove that minimum of two exponential random variables is another exponential random variable?
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20
Let $a_{i} \in\mathbb{R}$ ($i=1,2,\dots,n$), and $f(x)=\sum_{i=0}^{n}a_{i}x^i$ such that if $|x|\leqslant 1$, then $|f(x)|\leqslant 1$. Prove that:
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17
Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
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15
Prove that $2^n-3$ is squarefree
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14
$f(x)$ with real co-efficient and degree 2011 there is a real number $b$ such that $f(b)=f'(b)$
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13
Prove that $\phi(n) \geq \sqrt{n}/2$
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12
Galois group of a biquadratic quartic
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12
When is a sum of consecutive squares equal to a square?
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12
How to represent Fermat number $F_n$ as a sum of three squares?
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12
what is the sum of this?$\frac12+ \frac13+\frac14+\frac15+\frac16 +\dots\frac{1}{2012}+\frac{1}{2013} $
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11
Algebra Iranian Olympiad Problem
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11
How to find the eigenvalues and Jordan canonical form of this matrix
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11
How find this determinant $\det(\cos^4{(i-j)})_{n\times n}$
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11
symplectic lie algebra is simple
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10
Find the value of $a+b+c$
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10
convergence in probability induced by a metric
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10
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
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10
Prove:$A B$ and $B A$ has the same characteristic polynomial.
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10
How does (21) factor into prime ideals in the ring $\mathbb{Z}[\sqrt{-5}]$?
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10
Prove that $g(x)=\frac{\ln(S_n (x))}{\ln(S_{n-1}(x))}$ is increasing in $x$, where $S_{n}(x)=\sum_{m=0}^{n}\frac{x^m}{m!}$
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10
Polynomials invariant under the action of $S_m \times S_n$
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10
Integers expressible in the form $x^2 + 3y^2$
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10
Is $\ a^b+b^a\ $ transcendental if $\ a^b\ $ and $\ b^a\ $ are?
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10
Understanding the proof of Schur-Weyl Duality
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10
Does $2x^2-1=y^5$ have a solution in integers, with $y>1$?
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9
Countability of the zero set of a real polynomial
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9
How prove that polynomial has only real root.
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