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Utilizing AM $\ge$ GM in third, less obvious question

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#problem-solving
42
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How to approach this algebraic problem

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#problem-solving
81
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Let $z_i=\frac{y_i}n\sum_{j=1}^nx_j+\frac{x_i}n\sum_{j=1}^ny_j-x_iy_i$ with $|x_i|=|y_i|=1$. Prove that $\sum_{i=1}^n |z_i| \leq n$.

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#inequality #complex-numbers #problem-solving #absolute-value
50
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General method for determining binary function

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#functions #problem-solving #binary
81
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Sequence of functions converges

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#real-analysis #examples-counterexamples #uniform-convergence #problem-solving #pointwise-convergence
77
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textbook and exercises on using probabilistic methods to solve problems?

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#probability #reference-request #problem-solving #information-theory
45
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Probibility extended response question

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#probability-theory #probability-distributions #problem-solving #conditional-probability
247
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Rearranging the Diode Equation

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#problem-solving
58
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Find all the numbers and aware

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#number-theory #modular-arithmetic #contest-math #arithmetic #problem-solving
82
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Four points, two distance problem. How to solve this problem formally and computationally without manual plotting and and playing.

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#geometry #problem-solving #computational-geometry #plane-geometry
114
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Find the minimum of :$P=a+b+c-ab-bc-ca$

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#algebra-precalculus #proof-verification #systems-of-equations #problem-solving
77
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Calcule $\frac{x^3}{3}+\frac{48}{x^2}=10\left(\frac{x}{3}-\frac{4}{x} \right)$

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#algebra-precalculus #problem-solving
47
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Digit problem $a,b$

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#number-theory #systems-of-equations #contest-math #problem-solving #decimal-expansion
142
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What is the strategy to always win?

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#proof-verification #logic #arithmetic #problem-solving
52
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Eigenvectors of 2 matrix with the same eigenvalues

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#linear-algebra #problem-solving

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