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Floor sum function

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#number-theory #ceiling-and-floor-functions
53
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Prove that $A_i$ has at least $1$ member that is not colored.

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#contest-math #combinations #ceiling-and-floor-functions #extremal-combinatorics #hypergraphs
566
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When is $\lfloor x^n\rfloor$ a perfect square for all integers $n\geq 1$?

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#elementary-number-theory #ceiling-and-floor-functions #square-numbers
130
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Solving $ \left \lfloor \frac{x^2 + \left(n+1\right)x+n}{6x} \right \rfloor - \left \lceil \frac{x^2 + 2x+n}{6x} \right \rceil = \frac{n-1}{6} $

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#roots #ceiling-and-floor-functions
43
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Minimize a sum over permutations

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#optimization #summation #permutations #ceiling-and-floor-functions
64
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Range of values of $k$ in floor function

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#algebra-precalculus #ceiling-and-floor-functions
76
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How to find a closed form of $\displaystyle A_n=\sum_{k=1}^n\left\lfloor\varphi\sqrt k\right\rfloor$?

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#calculus #summation #ceiling-and-floor-functions
63
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What is the Meaning of Mathematical Operator That There is a Bulge in the Lower Part of The Absolute Operator

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#notation #ceiling-and-floor-functions
68
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Proof $\displaystyle \sum_{k=0}^n \lfloor \varphi^k\rfloor=\left\lfloor\dfrac{\varphi^{n+1}-1}{\varphi-1}-\dfrac{n-1+(-1)^n}{2}\right\rfloor$

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#summation #ceiling-and-floor-functions
96
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Proof of $\left|\sum_{k=2}^n \lfloor k^{\varphi-1}\rfloor-B_n\right|\le 2$

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#calculus #summation #ceiling-and-floor-functions
39
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Integer part of positive integral multiples of the cube root of 3.

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#ceiling-and-floor-functions
32
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Reasoning about floor functions and successive squares

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#elementary-number-theory #inequality #ceiling-and-floor-functions
65
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If $|x| \le 8$, find the number of real solutions to equation $x^2 + x - \lfloor x \rfloor - \lfloor x^2 \rfloor = 1$

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#ceiling-and-floor-functions
60
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Right Hand Limit involving fractional part

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#calculus #limits #ceiling-and-floor-functions #fractional-part
54
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The slope and deviation from the trend line of a sum of floor-of-fraction step functions $f(x) = \left\lfloor\frac{x - r}{d} \right\rfloor$

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#real-analysis #elementary-number-theory #inequality #integers #ceiling-and-floor-functions

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