Question

Calculate the minimum value of an integer $x$, such that $\left\lfloor\frac{xy^2}{xy+w(y-z)}\right\rfloor>z$

score 38 · Answer 1 · 2022-01-07 08:52:23

Calculate the minimum value of an integer $x$, such that $\left\lfloor\frac{xy^2}{xy+w(y-z)}\right\rfloor>z$

Published on 07 Jan 2022 - 8:52

score 97 · Answer 2 · 2022-01-07 17:09:57

Is $\lfloor{\frac{a+b+c+d}{4}}\rfloor=\lfloor\frac{\lfloor{\frac{a+b}{2}}\rfloor+\lfloor{\frac{c+d}{2}}\rfloor}{2}\rfloor$ for $a,b,c,d\in\mathbb R$?

score 191 · Answer 3 · 2022-01-11 09:23:41

191

Views

Solving $4\lfloor x \rfloor=x+\{x\}$. What is wrong in my solution? Can anyone tell?

Published on 11 Jan 2022 - 9:23

score 5.4k · Answer 4 · 2026-02-23 08:34:01

5.4k

Views

Is there a function that is the envelope of the sum of ceilings of reciprocal functions

Published on 23 Feb 2026 - 8:34

score 178 · Answer 5 · 2022-01-22 17:16:45

modulus, floor, quotient $a = qM + r,\; q = \big\lfloor \frac{a}{M} \big\rfloor,\; 0 \leq r < M,\; r = a \bmod M$ are not self-consistent when $M < 0$

score 127 · Answer 6 · 2022-01-23 21:52:54

Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$ Find the number of possible values of $f(x)$ for $0 \le x \le 10.$

score 1.1k · Answer 7 · 2022-01-23 22:32:05

1.1k

Views

Does Euclidean division still produce unique quotient and remainder when the dividend and divisor are real numbers?

Published on 23 Jan 2022 - 22:32

score 77 · Answer 8 · 2022-01-24 20:43:09

Is there an equivalence between $\big\lceil \frac{a}{M} \big\rceil$ and $floor$ that works regardless of wether $a$ and/or $M$ are integers or not?

score 35 · Answer 9 · 2022-01-28 21:26:29

Can we express $\lfloor\frac{a+b}M\rfloor$ and $\lceil\frac{a+b}M\rceil$ in simpler terms? Eg in terms of $\lfloor\frac aM\rfloor, a\bmod M, b$, etc?

score 65 · Answer 10 · 2026-02-24 03:30:41

65

Views

Solving summation of fractional powers with floor

Published on 24 Feb 2026 - 3:30

score 101 · Answer 11 · 2022-02-02 13:03:51

101

Views

How to solve floor(x/2) · ceil (2/x) = 17?

Published on 02 Feb 2022 - 13:03

score 52 · Answer 12 · 2022-02-04 11:38:41

52

Views

Closed form of sum of function defined on a mod operator

Published on 04 Feb 2022 - 11:38

score 249 · Answer 13 · 2022-02-05 06:40:22

249

Views

How to find floor of $ 1+\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{4}} + ...+\frac{1}{\sqrt{2017}}$?

Published on 05 Feb 2022 - 6:40

score 56 · Answer 14 · 2022-02-06 13:44:08

56

Views

Limit of a function with two floor functions in the expression

Published on 06 Feb 2022 - 13:44

score 48 · Answer 15 · 2026-03-30 15:50:51

48

Views

Change of variable in a summation with the floor function

Published on 30 Mar 2026 - 15:50

List Question

Calculate the minimum value of an integer $x$, such that $\left\lfloor\frac{xy^2}{xy+w(y-z)}\right\rfloor>z$

Is $\lfloor{\frac{a+b+c+d}{4}}\rfloor=\lfloor\frac{\lfloor{\frac{a+b}{2}}\rfloor+\lfloor{\frac{c+d}{2}}\rfloor}{2}\rfloor$ for $a,b,c,d\in\mathbb R$?

Solving $4\lfloor x \rfloor=x+\{x\}$. What is wrong in my solution? Can anyone tell?

Is there a function that is the envelope of the sum of ceilings of reciprocal functions

modulus, floor, quotient $a = qM + r,\; q = \big\lfloor \frac{a}{M} \big\rfloor,\; 0 \leq r < M,\; r = a \bmod M$ are not self-consistent when $M < 0$

Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$ Find the number of possible values of $f(x)$ for $0 \le x \le 10.$

Does Euclidean division still produce unique quotient and remainder when the dividend and divisor are real numbers?

Is there an equivalence between $\big\lceil \frac{a}{M} \big\rceil$ and $floor$ that works regardless of wether $a$ and/or $M$ are integers or not?

Can we express $\lfloor\frac{a+b}M\rfloor$ and $\lceil\frac{a+b}M\rceil$ in simpler terms? Eg in terms of $\lfloor\frac aM\rfloor, a\bmod M, b$, etc?

Solving summation of fractional powers with floor

How to solve floor(x/2) · ceil (2/x) = 17?

Closed form of sum of function defined on a mod operator

How to find floor of $ 1+\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{4}} + ...+\frac{1}{\sqrt{2017}}$?

Limit of a function with two floor functions in the expression

Change of variable in a summation with the floor function

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