List questions from problem-solving

Published on 14 Apr 2026 - 23:38

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Car A is 50km east of car B and begins moving west at 50km/h. Simultaneously, car B begins moving north at 90km/h. Find:

Published on 11 Apr 2026 - 3:21

173

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Let $R$ be the set $\mathbb{R}$ of all real numbers with the co-finite topology. How can one show that $R$ is contractible?

Published on 16 Apr 2026 - 14:51

45

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Wave equation, finding a constant that solves the equation?

Published on 08 Apr 2026 - 19:47

404

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Proof of $ASA$ criterium

Published on 10 Apr 2026 - 2:50

391

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What does "parity pattern" mean?

Published on 12 Apr 2026 - 3:09

434

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Probability that the sum of two integers in $\{1,\dots,n\}$ equals a perfect square

Published on 12 Apr 2026 - 19:16

129

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Pr. 5 of chapter 1 of Walter Rudin.

Published on 15 Apr 2026 - 14:52

25

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Analysis of a particular instance of a non-linearsystem of equations

Published on 11 Apr 2026 - 5:24

91

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prove that $\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\dots+\sqrt{2}}}}}_{\text{n radicals}}=2\cos{\frac{\pi}{2^{n+1}}}$

Published on 17 Apr 2026 - 16:03

146

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Is it true that $\gcd(p+1,pk)=1$.

Published on 14 Apr 2026 - 7:55

485

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Angle at intersection by diagonals of a quadrilateral

Published on 15 Apr 2026 - 0:23

84

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If $(b + c) , (c + a) , (a + b)$ are in H.P. then find the relation between $\dfrac{a}{b+c} , \dfrac{b}{c+a} , \dfrac{c}{a+b}$ .

Published on 12 Apr 2026 - 0:37

125

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Integrating $\int^u_0\frac{dx}{x^2+3x+2}$

Published on 15 Apr 2026 - 23:32

766

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Sum of power series $\frac{x^{2n-1}}{2n-1}$

Published on 14 Apr 2026 - 6:20

List Question

Let $a = 2019^{1009} , b = 2019!$ and $c = 1010^{2019}$

Car A is 50km east of car B and begins moving west at 50km/h. Simultaneously, car B begins moving north at 90km/h. Find:

Let $R$ be the set $\mathbb{R}$ of all real numbers with the co-finite topology. How can one show that $R$ is contractible?

Wave equation, finding a constant that solves the equation?

Proof of $ASA$ criterium

What does "parity pattern" mean?

Probability that the sum of two integers in $\{1,\dots,n\}$ equals a perfect square

Pr. 5 of chapter 1 of Walter Rudin.

Analysis of a particular instance of a non-linearsystem of equations

prove that $\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\dots+\sqrt{2}}}}}_{\text{n radicals}}=2\cos{\frac{\pi}{2^{n+1}}}$

Is it true that $\gcd(p+1,pk)=1$.

Angle at intersection by diagonals of a quadrilateral

If $(b + c) , (c + a) , (a + b)$ are in H.P. then find the relation between $\dfrac{a}{b+c} , \dfrac{b}{c+a} , \dfrac{c}{a+b}$ .

Integrating $\int^u_0\frac{dx}{x^2+3x+2}$

Sum of power series $\frac{x^{2n-1}}{2n-1}$

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