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A question about IMO 1986 P3

score 549 · Answer 1 · 2026-03-25 07:47:32

549

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A question about IMO 1986 P3

Published on 25 Mar 2026 - 7:47

score 537 · Answer 2 · 2026-03-25 07:45:42

537

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Points A, B and C on a circle of radius r are situated so that AB = AC, AB > r, and the length of minor arc BC is r.

Published on 25 Mar 2026 - 7:45

score 81 · Answer 3 · 2018-08-03 16:08:48

81

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Proving a line perpendicular to another in a circle

Published on 03 Aug 2018 - 16:08

score 148 · Answer 4 · 2026-03-26 01:12:14

148

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Determining all $f : \Bbb R \to\Bbb R$ satisfying $f\bigl(f(x)f(y)\bigr)+f(x+y)=f(xy)$

Published on 26 Mar 2026 - 1:12

score 167 · Answer 5 · 2018-08-04 17:43:48

167

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Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$

Published on 04 Aug 2018 - 17:43

score 153 · Answer 6 · 2018-08-04 22:12:06

153

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From book : Putnam and beyond

Published on 04 Aug 2018 - 22:12

score 394 · Answer 7 · 2026-03-25 13:59:04

394

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Putnam 1985 B5 Integration by Substitution

Published on 25 Mar 2026 - 13:59

score 128 · Answer 8 · 2018-08-05 20:25:31

For $a$, $b$, $c$ distinct integers, and $P$ a polynomial with integer coefficients, $P(a)=b$, $P(b)=c$, $P(c)=a$ cannot be satisfied simultaneously

score 121 · Answer 9 · 2018-08-05 21:13:26

121

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Putnam and Beyond (Methods of proof) Problem 20

Published on 05 Aug 2018 - 21:13

score 157 · Answer 10 · 2018-08-06 12:24:40

157

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Ratio of angles in a triangle

Published on 06 Aug 2018 - 12:24

score 88 · Answer 11 · 2018-08-09 06:08:07

88

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Filling in a square with 1,2,3 such that in every row, column, diagonal divisible by 3, there are equal number of 1s, 2s, and 3s

Published on 09 Aug 2018 - 6:08

score 148 · Answer 12 · 2018-08-09 18:22:13

148

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Putnam and Beyond: Problem 87 (Matrices and algebra)

Published on 09 Aug 2018 - 18:22

score 333 · Answer 13 · 2018-08-10 07:49:48

333

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Find all polynomials $P(x) \in \mathbb{Z}[x]$ such that if $P(s)$ and $P(t)$ are both integers, then $P(s+t)$ is also an integer

Published on 10 Aug 2018 - 7:49

score 84 · Answer 14 · 2026-03-25 16:02:22

84

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A direct way to an inequality : Ferrari's identities

Published on 25 Mar 2026 - 16:02

score 3.1k · Answer 15 · 2018-08-11 17:27:18

3.1k

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What does it mean for points to be picked uniformly and independently?

Published on 11 Aug 2018 - 17:27

List Question

A question about IMO 1986 P3

Points A, B and C on a circle of radius r are situated so that AB = AC, AB > r, and the length of minor arc BC is r.

Proving a line perpendicular to another in a circle

Determining all $f : \Bbb R \to\Bbb R$ satisfying $f\bigl(f(x)f(y)\bigr)+f(x+y)=f(xy)$

Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$

From book : Putnam and beyond

Putnam 1985 B5 Integration by Substitution

For $a$, $b$, $c$ distinct integers, and $P$ a polynomial with integer coefficients, $P(a)=b$, $P(b)=c$, $P(c)=a$ cannot be satisfied simultaneously

Putnam and Beyond (Methods of proof) Problem 20

Ratio of angles in a triangle

Filling in a square with 1,2,3 such that in every row, column, diagonal divisible by 3, there are equal number of 1s, 2s, and 3s

Putnam and Beyond: Problem 87 (Matrices and algebra)

Find all polynomials $P(x) \in \mathbb{Z}[x]$ such that if $P(s)$ and $P(t)$ are both integers, then $P(s+t)$ is also an integer

A direct way to an inequality : Ferrari's identities

What does it mean for points to be picked uniformly and independently?

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