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On Arthur Engel Book, First Chapter : Invariance

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#sequences-and-series #inequality #problem-solving #a.m.-g.m.-inequality #invariance
400
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Hartshorne's Ex. 3.15 (chap. 1) Product affine varieties

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#algebraic-geometry #problem-solving #affine-varieties
120
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Equation of circle tangent to a circle and a line

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#algebra-precalculus #analytic-geometry #circles #problem-solving
291
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Find all pairs of positive rationals $(a, b)$ with $\frac{ab+1}{a}$, $\frac{ab+1}{b}$ both integers

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#elementary-number-theory #proof-explanation #contest-math #problem-solving #intuition
47
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Let $P(x^{3})=ax^{6}+(b-2)x^{5}+(a+3)x^{4}+bx^{3}+3$ be a polynomial.Then, what is the remainder when $P(x)$ is divided by $(x-3)$

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#polynomials #problem-solving
96
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How many ways can n married couples sit at a round table in such a way that there is one man between every two women and no man is seated next to wife

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#combinatorics #permutations #problem-solving #inclusion-exclusion
187
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how to solve rational problem solving question

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#probability #problem-solving
45
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puzzle solving question

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#probability #logic #problem-solving
30
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particular part of non-linear second order ODE

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#ordinary-differential-equations #problem-solving #mathematical-physics #general-relativity #nonlinear-analysis
134
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Proving an existence using mean value theorem.

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#calculus #problem-solving
74
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Let $p, m, n$ be positive integers. Determine the number of m by n matrices with entries from the set ${1,2,...,p}$ which have a certain property

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#combinatorics #matrices #permutations #problem-solving #inclusion-exclusion
111
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Proving this function to be identically 0

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#complex-analysis #problem-solving
50
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Write an entire function in terms of 2 entire functions

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#complex-analysis #problem-solving #entire-functions
350
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Shrinking Squares. Emipirical exploration

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#sequences-and-series #algorithms #contest-math #problem-solving
35
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Find the real values of $m$ such that $a \leq b \leq c$ .

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#linear-algebra #problem-solving

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