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Parallelism Alert's user avatar
Parallelism Alert's user avatar
Parallelism Alert's user avatar
Parallelism Alert
  • Member for 5 years, 10 months
  • Last seen more than 3 years ago
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question
12
If $|g(a)-g(b)| \leq |f(a)-f(b)|,$ for every $a,b$, and $f$ is a Darboux function, then $g$ is a Darboux function.
Mar 9, 2020
question
7
Show $p^5$ divides $\binom{p^2}{p} -p $, for all primes $p\ge 5$
Apr 15, 2019
question
5
$ A^2 - B^2 = I_{2n+1} \implies det(AB-BA)=0 $ where A,B are complex matrices of odd size
Jan 27, 2020
question
3
Prove there are infinitely many (x, y, z) positive integers satisfying $x^5 + y^7 = z^9$
Jan 30, 2019
question
3
Prove that $z_1,z_2,z_3$ with equal, non-zero modulus, are vertices of an equilateral triangle if and only if $\sum_{cyc}|z_1-z_2|(z_1+z_2) = 0 $
Feb 12, 2019
answer
3
Find the number of ordered triplets satisfying $5\left(x+\frac{1}{x}\right)=12\left(y+\frac{1}{y}\right)=13\left(z+\frac{1}{z}\right)$
Mar 3, 2019
question
2
Prove that $ (\frac{\sum_{i=1}^n x_i}{n})^{\sum_{i=1}^n x_i} \le \prod_{i=1}^n {x_i}^{x_i}$ $, \forall x_i>0, n\ge1 $
Feb 9, 2019
question
2
Prove that in every triangle the inequality $a^3r_a + b^3r_b + c^3r_c \ge 8S(2R-r)^2 $ takes place
Mar 3, 2019
question
2
If A is a square matrix of size n with real entries, with $A = A^{p+1}$, then $rank(A) + rank (I_n - A^p) = n$
Feb 5, 2020
question
2
Find all $n$ for which there exist A, B, matrices of size n with real entries, such that $A^2B-BA^2=A$.
Mar 6, 2020