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Number theory question with floor function

score 764 · Answer 1 · 2026-03-25 15:56:41

764

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Number theory question with floor function

Published on 25 Mar 2026 - 15:56

score 67 · Answer 2 · 2018-07-23 06:09:36

67

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Fundamental Solution for this Problem Solving Question

Published on 23 Jul 2018 - 6:09

score 115 · Answer 3 · 2018-07-23 10:19:35

115

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Effectively reconstructing all original 5-tuples from a subset of their respective 4-tuples

Published on 23 Jul 2018 - 10:19

score 222 · Answer 4 · 2026-03-26 14:34:27

222

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If $ab \mid c(c^2-c+1)$ and $c^2+1 \mid a+b$ then prove that $\{a, b\}=\{c, c^2-c+1 \}$

Published on 26 Mar 2026 - 14:34

score 88 · Answer 5 · 2018-07-25 18:14:27

88

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$2010$ $G1$, proving quadrilateral concyclic

Published on 25 Jul 2018 - 18:14

score 84 · Answer 6 · 2026-03-25 21:01:38

84

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How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

Published on 25 Mar 2026 - 21:01

score 206 · Answer 7 · 2026-03-25 00:04:25

206

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Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Published on 25 Mar 2026 - 0:04

score 754 · Answer 8 · 2018-07-27 09:14:06

754

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Proving $10240...02401$ composite

Published on 27 Jul 2018 - 9:14

score 159 · Answer 9 · 2018-07-27 09:56:41

159

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Find an integer $a$ such that $(x-a)(x-10)+1=(x-b)(x-c)$ for some integers $b$ and $c$

Published on 27 Jul 2018 - 9:56

score 79 · Answer 10 · 2026-03-25 14:24:37

79

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AIME I 2000 Problem 8: Calculating the height of the liquid given Fraction of the Volume

Published on 25 Mar 2026 - 14:24

score 128 · Answer 11 · 2018-07-30 06:40:47

128

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Prove $\sqrt{x^2+1} + \frac{1}{\sqrt{x^2 +1}}\geq 2$

Published on 30 Jul 2018 - 6:40

score 651 · Answer 12 · 2026-03-25 06:06:36

651

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Making the sum of 5th power of integers, a perfect square.

Published on 25 Mar 2026 - 6:06

score 332 · Answer 13 · 2026-03-25 12:52:25

332

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Solution to Putnam 2007 A-1

Published on 25 Mar 2026 - 12:52

score 848 · Answer 14 · 2018-07-30 17:06:29

848

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Prove that $\frac{21n+4}{14n+3}$ is in lowest terms for any natural $n$.

Published on 30 Jul 2018 - 17:06

score 1.1k · Answer 15 · 2026-03-25 06:12:13

1.1k

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Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Published on 25 Mar 2026 - 6:12

List Question

Number theory question with floor function

Fundamental Solution for this Problem Solving Question

Effectively reconstructing all original 5-tuples from a subset of their respective 4-tuples

If $ab \mid c(c^2-c+1)$ and $c^2+1 \mid a+b$ then prove that $\{a, b\}=\{c, c^2-c+1 \}$

$2010$ $G1$, proving quadrilateral concyclic

How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Proving $10240...02401$ composite

Find an integer $a$ such that $(x-a)(x-10)+1=(x-b)(x-c)$ for some integers $b$ and $c$

AIME I 2000 Problem 8: Calculating the height of the liquid given Fraction of the Volume

Prove $\sqrt{x^2+1} + \frac{1}{\sqrt{x^2 +1}}\geq 2$

Making the sum of 5th power of integers, a perfect square.

Solution to Putnam 2007 A-1

Prove that $\frac{21n+4}{14n+3}$ is in lowest terms for any natural $n$.

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

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