Question

Solving Diophatine Equations

score 68 · Answer 1 · 2019-06-22 06:31:30

68

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Solving Diophatine Equations

Published on 22 Jun 2019 - 6:31

score 117 · Answer 2 · 2019-06-22 15:12:52

117

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Olympiad inequality :$2\sqrt{(x^xy^y)^{\frac{1}{x+y}}\sqrt{xy}}\leq \frac{x+y}{2}$ for $x,y>0$

Published on 22 Jun 2019 - 15:12

score 101 · Answer 3 · 2019-06-23 02:18:14

101

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Determine the numbers of solutions of equations $\sin v= \frac{v}{1964}$ and $\sin v= \log_{100} v$ .

Published on 23 Jun 2019 - 2:18

score 4.9k · Answer 4 · 2019-06-23 08:19:05

4.9k

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What are the last two digits of $2017^{2017}$?

Published on 23 Jun 2019 - 8:19

score 150 · Answer 5 · 2019-06-23 10:54:48

150

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$ 5r + 4s + 3t + 6u = 100, \:\: r \ge s \ge t \ge u \ge 0 $ maximum and minimum possible of $r + s + t + u$?

Published on 23 Jun 2019 - 10:54

score 301 · Answer 6 · 2019-06-24 15:43:45

301

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Show that $p'(c)+100p(c)=0$

Published on 24 Jun 2019 - 15:43

score 138 · Answer 7 · 2026-03-25 09:28:55

138

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Find an example of a set of points of the plane such that there exist at least $2^{n-2}$ good partitions.

Published on 25 Mar 2026 - 9:28

score 911 · Answer 8 · 2019-06-24 17:31:10

911

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Probability question from British Math Olympiad, 1973

Published on 24 Jun 2019 - 17:31

score 419 · Answer 9 · 2026-03-26 22:14:52

419

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Prove that $\sum\limits_{cyc}\sqrt{a+11bc+6}\geq9\sqrt2.$

Published on 26 Mar 2026 - 22:14

score 103 · Answer 10 · 2019-06-25 12:18:43

103

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APMO Problem Solution

Published on 25 Jun 2019 - 12:18

score 532 · Answer 11 · 2026-03-25 11:02:28

532

Views

Packing of parallelograms with sides $1$ and $\sqrt{2}$ and angle $45^{\circ}$ in a rectangular container

Published on 25 Mar 2026 - 11:02

score 408 · Answer 12 · 2019-06-25 22:07:24

408

Views

Surface area of spheres not seen by any other.

Published on 25 Jun 2019 - 22:07

score 327 · Answer 13 · 2019-06-26 05:59:09

327

Views

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

Published on 26 Jun 2019 - 5:59

score 134 · Answer 14 · 2019-06-26 17:45:28

134

Views

Winning strategy of game with positive divisors of the number $10^{2n}$

Published on 26 Jun 2019 - 17:45

score 1k · Answer 15 · 2026-02-23 06:41:02

1k

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Guaranteed to guess two numbers in one from twelve lottery tickets, if falls $6$ balls with numbers from $1$ to $36$

Published on 23 Feb 2026 - 6:41

List Question

Solving Diophatine Equations

Olympiad inequality :$2\sqrt{(x^xy^y)^{\frac{1}{x+y}}\sqrt{xy}}\leq \frac{x+y}{2}$ for $x,y>0$

Determine the numbers of solutions of equations $\sin v= \frac{v}{1964}$ and $\sin v= \log_{100} v$ .

What are the last two digits of $2017^{2017}$?

$ 5r + 4s + 3t + 6u = 100, \:\: r \ge s \ge t \ge u \ge 0 $ maximum and minimum possible of $r + s + t + u$?

Show that $p'(c)+100p(c)=0$

Find an example of a set of points of the plane such that there exist at least $2^{n-2}$ good partitions.

Probability question from British Math Olympiad, 1973

Prove that $\sum\limits_{cyc}\sqrt{a+11bc+6}\geq9\sqrt2.$

APMO Problem Solution

Packing of parallelograms with sides $1$ and $\sqrt{2}$ and angle $45^{\circ}$ in a rectangular container

Surface area of spheres not seen by any other.

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

Winning strategy of game with positive divisors of the number $10^{2n}$

Guaranteed to guess two numbers in one from twelve lottery tickets, if falls $6$ balls with numbers from $1$ to $36$

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