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Mathematics
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nowepas
  • Member for 3 years, 2 months
  • Last seen more than 2 years ago
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13
Finding all functions $f: \mathbb{Z^{+}}\to \mathbb{Z^{+}}$ such that $f(a)| (f(b)+a-b)$ for all $a,b\in \mathbb{Z^{+}}$
May 13, 2021
6
Prove that if $x_{1}x_{2}...x_{n}=1$ then $\frac{1}{1+x_{1}+x_{1}x_{2}}+...+\frac{1}{1+x_{n-1}+x_{n-1}x_{n}}+\frac{1}{1 +x_{n}+x_{n}x_{1}}\ge 1$ [duplicate]
Nov 6, 2021
4
Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $\gcd(f(m),n) + \text{lcm}(m,f(n)) = \text{lcm}(f(m),n) + \gcd(m,f(n))$
Jan 24, 2022
3
Prove that in quadrilateral $ABCD$, $|\angle DAB|=|\angle ABC|=|\angle BCD|$, $|DA|=|DC|$, if $|BE|=|DA|$, $CE$ is the angle bisector of $\angle BCD$
Jun 24, 2021