List questions from ceiling-and-floor-functions

Published on 11 Sep 2016 - 10:12

156

Views

Prove that $\binom{k}{p} \equiv \left\lfloor \frac{k}{p} \right\rfloor \pmod p$ for all odd prime number $p$ and $k\ge 3$

Published on 12 Sep 2016 - 20:02

140

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Prove that $\lfloor(n+1)a\rfloor-1$ is divisible by $(n+1)$ if $n= \left\lfloor \frac {1}{ a- \lfloor a \rfloor } \right\rfloor$

Published on 13 Sep 2016 - 13:24

377

Views

Prove ceiling function is lower semicontinuous

Published on 13 Mar 2026 - 23:16

51

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Finding the minimum of an integer part

Published on 13 Sep 2016 - 14:28

316

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Proof of a property of Greatest Integer Function

Published on 14 Sep 2016 - 5:40

653

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When $\lfloor{ab}\rfloor = \lfloor{a}\rfloor\lfloor{b}\rfloor$

Published on 14 Sep 2016 - 18:21

194

Views

Multiple of real numbers with only $0$'s and $1$'s in the integer part

Published on 29 Mar 2026 - 15:15

154

Views

What is the relation between $\lfloor x+y \rfloor$ and $\lfloor x \rfloor + \lfloor y\rfloor$ for any reals $x,y$

Published on 18 Sep 2016 - 13:20

93

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unique floor value proof

Published on 19 Sep 2016 - 13:40

98

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If $x\lt y$ then prove that $\lfloor x\rfloor \leq \lfloor y\rfloor $.

Published on 19 Sep 2016 - 18:01

152

Views

Showing that a function is discontinuous

Published on 23 Sep 2016 - 19:13

347

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Evaluating the Limit of a Sum of Floor Functions

Published on 24 Sep 2016 - 6:22

281

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What is the indefinite integral of $\lfloor x^{-1} \rfloor$?

Published on 25 Mar 2026 - 14:46

110

Views

Evaluate the limit $\lim_{x\to0^-}\frac{\sin\lfloor x\rfloor}x$

Published on 28 Sep 2016 - 15:06

List Question

A number theory exercise involving the floor function

Prove that $\binom{k}{p} \equiv \left\lfloor \frac{k}{p} \right\rfloor \pmod p$ for all odd prime number $p$ and $k\ge 3$

Prove that $\lfloor(n+1)a\rfloor-1$ is divisible by $(n+1)$ if $n= \left\lfloor \frac {1}{ a- \lfloor a \rfloor } \right\rfloor$

Prove ceiling function is lower semicontinuous

Finding the minimum of an integer part

Proof of a property of Greatest Integer Function

When $\lfloor{ab}\rfloor = \lfloor{a}\rfloor\lfloor{b}\rfloor$

Multiple of real numbers with only $0$'s and $1$'s in the integer part

What is the relation between $\lfloor x+y \rfloor$ and $\lfloor x \rfloor + \lfloor y\rfloor$ for any reals $x,y$

unique floor value proof

If $x\lt y$ then prove that $\lfloor x\rfloor \leq \lfloor y\rfloor $.

Showing that a function is discontinuous

Evaluating the Limit of a Sum of Floor Functions

What is the indefinite integral of $\lfloor x^{-1} \rfloor$?

Evaluate the limit $\lim_{x\to0^-}\frac{\sin\lfloor x\rfloor}x$

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