Question

Given irrational numbers $0<\gamma_1<\gamma_2<1,$ real numbers $0\leq a<b\leq 1,$ does $\exists n$ such that $\{n\gamma_1\}, \{n\gamma_2\}\in(a,b)?$

score 64 · Answer 1 · 2026-04-16 00:52:48

64

Views

Given irrational numbers $0<\gamma_1<\gamma_2<1,$ real numbers $0\leq a<b\leq 1,$ does $\exists n$ such that $\{n\gamma_1\}, \{n\gamma_2\}\in(a,b)?$

Published on 16 Apr 2026 - 0:52

score 316 · Answer 2 · 2026-04-13 16:27:44

316

Views

How many equations are required to solve $n$ many variables?

Published on 13 Apr 2026 - 16:27

score 390 · Answer 3 · 2026-04-17 12:30:13

390

Views

Find $x,y,z$ satisfying $x(y+z-x)=68-2x^2$, $y(z+x-y)=102-2y^2$, $z(x+y-z)=119-2z^2$

Published on 17 Apr 2026 - 12:30

score 133 · Answer 4 · 2026-04-16 01:23:56

133

Views

Integration of $\int_0^\frac{\pi}{4} (\sin^6 2x+\cos^6 2x) \cdot\ln (1+\tan x) dx$

Published on 16 Apr 2026 - 1:23

score 95 · Answer 5 · 2026-04-14 09:42:33

95

Views

Let $1=n_0<n_1<\ldots$ be an increasing sequence of positive integers. True/False: $\sum_{i=1}^\infty\frac{n_{i+1}-n_i}{n_{i+1}}$ diverges to $\infty$

Published on 14 Apr 2026 - 9:42

score 97 · Answer 6 · 2026-04-20 10:30:22

97

Views

$\int_{-2}^xf(t)dt$ for $f(t) = \tiny\begin{cases} -1 \, &t<0 \\ 1 \, &t\ge 0 \end{cases} $, and its limit at $x=0$

Published on 20 Apr 2026 - 10:30

score 163 · Answer 7 · 2026-04-14 07:54:42

163

Views

Finding the maximum $k$ such that $(7!)!$ is divisible by $(7!)^{k!}\cdot(6!)!$

Published on 14 Apr 2026 - 7:54

score 58 · Answer 8 · 2026-04-14 01:46:19

58

Views

Which value a and e must have to meet the conditions?

Published on 14 Apr 2026 - 1:46

score 129 · Answer 9 · 2026-04-14 12:01:44

129

Views

(Borel-Cantelli) If $X_i$ is a sequence of identical and independent variables. Using Borel-Cantelli, prove that...

Published on 14 Apr 2026 - 12:01

score 24 · Answer 10 · 2026-04-09 10:57:36

24

Views

Finding product of three numbers given respective products

Published on 09 Apr 2026 - 10:57

score 26 · Answer 11 · 2026-04-16 18:06:33

26

Views

For Continuous $f: [1,4] \to \mathbb R$, $f(1)=f(4)$, Show $f(c) = f(c+ 1.5)$ for at least one c

Published on 16 Apr 2026 - 18:06

score 117 · Answer 12 · 2026-04-17 12:30:37

117

Views

Finding number of ways to put four balls in k bins

Published on 17 Apr 2026 - 12:30

score 144 · Answer 13 · 2026-04-12 05:13:25

144

Views

2n ambassadors are invited to a banquet

Published on 12 Apr 2026 - 5:13

score 258 · Answer 14 · 2026-04-12 13:02:02

258

Views

some questions about IMO 1986 problem 3

Published on 12 Apr 2026 - 13:02

score 106 · Answer 15 · 2026-04-13 05:57:19

106

Views

algorithms applied to n-tuples of numbers to end up with $(0,0,...,0)$

Published on 13 Apr 2026 - 5:57

List Question

Given irrational numbers $0<\gamma_1<\gamma_2<1,$ real numbers $0\leq a<b\leq 1,$ does $\exists n$ such that $\{n\gamma_1\}, \{n\gamma_2\}\in(a,b)?$

How many equations are required to solve $n$ many variables?

Find $x,y,z$ satisfying $x(y+z-x)=68-2x^2$, $y(z+x-y)=102-2y^2$, $z(x+y-z)=119-2z^2$

Integration of $\int_0^\frac{\pi}{4} (\sin^6 2x+\cos^6 2x) \cdot\ln (1+\tan x) dx$

Let $1=n_0<n_1<\ldots$ be an increasing sequence of positive integers. True/False: $\sum_{i=1}^\infty\frac{n_{i+1}-n_i}{n_{i+1}}$ diverges to $\infty$

$\int_{-2}^xf(t)dt$ for $f(t) = \tiny\begin{cases} -1 \, &t<0 \\ 1 \, &t\ge 0 \end{cases} $, and its limit at $x=0$

Finding the maximum $k$ such that $(7!)!$ is divisible by $(7!)^{k!}\cdot(6!)!$

Which value a and e must have to meet the conditions?

(Borel-Cantelli) If $X_i$ is a sequence of identical and independent variables. Using Borel-Cantelli, prove that...

Finding product of three numbers given respective products

For Continuous $f: [1,4] \to \mathbb R$, $f(1)=f(4)$, Show $f(c) = f(c+ 1.5)$ for at least one c

Finding number of ways to put four balls in k bins

2n ambassadors are invited to a banquet

some questions about IMO 1986 problem 3

algorithms applied to n-tuples of numbers to end up with $(0,0,...,0)$

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