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ami_ba

Math, math and only math

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  • Kolkata, West Bengal, India
  • Member for 5 years, 5 months
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  • Last seen Jul 8 '20 at 19:09

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8 How to prove that $\frac{1000!}{(500!)^2}$ is not divisible by 7? Jan 24 '17
8 Find all odd solutions for $n$ for which $3n^2+8$ is equal to a number in base $10$ which is formed by only one digit(e.g.-$222,8888888,4,99$ etc.) Jun 25 '18
7 Solving these two equations Oct 21 '17
7 For positve $a$, $b$, $c$, $d$ with $a+b+c+d\leq 1$, prove that $\sqrt[4]{(1-a^4)(1-b^4)(1-c^4)(1-d^4)}\geq255\cdot a b c d .$ Sep 25 '18
5 Prove that $x^2 y+ y^2 z + z^2x ≥ 2(x + y + z) − 3$ Oct 14 '17
5 Solving without using of Lagrange multipliers Oct 19 '17
5 If $a,b,c$ are positive reals, then prove that $(a+b)(a+c)\ge 2 \sqrt {abc(a+b+c)}$ Sep 19 '17
4 If $\alpha,a,b$ are integers and $b\neq-1$, then prove that, if $\alpha$ satisfies the equation $x^2+ax+b+1=0$, $a^2+b^2$ must be composite. Sep 30 '17
4 Prove that for every pair of coprime positive integers $p,q$, $(x^{pq}-1)(x-1)$ is divisible by $(x^p-1)(x^q-1)$. Jul 13 '17
4 What is the maximum number of distinct positive integer's square that sums up to $2002$? Jul 14 '17
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