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Calculate the number of nonnegative integer solutions of $ax+by\leq c$.

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#combinatorics #diophantine-equations #ceiling-and-floor-functions #combinatorial-geometry #integer-lattices
85
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For $s, t \in \{-\lfloor (n-1)/2 \rfloor, \dots, -1, 0, 1, \dots, \lfloor n/2 \rfloor \}$, $n \in \mathbb{Z}_{ > 0}$, show $s-t \neq \ell n$

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#induction #integers #ceiling-and-floor-functions
1.5k
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How to solve a recurrence relation involving a ceiling function?

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#recurrence-relations #ceiling-and-floor-functions
825
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Constructing a 2-periodic extension of the absolute value function using floor and ceiling functions

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#ceiling-and-floor-functions
168
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Calculating $\sum_{k=0}^{\lfloor \frac{p}{2} \rfloor} \binom{p}{k}$

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#summation #binomial-coefficients #ceiling-and-floor-functions
66
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Mircea Merca's conjecteture

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#sequences-and-series #ceiling-and-floor-functions
675
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Limit of a sequence with floor function.

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#calculus #limits #ceiling-and-floor-functions
401
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Prove a limit involving the ceiling function

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#number-theory #limits #irrational-numbers #ceiling-and-floor-functions
144
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Algorithm for finding sequence verifying a floor equation

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#optimization #algorithms #ceiling-and-floor-functions
106
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Does $\left\lfloor\frac{x^2+x}{i}\right\rfloor - \left\lfloor\frac{x^2}{i}\right\rfloor = \left\lfloor\frac{x}{i}\right\rfloor$?

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#proof-verification #ceiling-and-floor-functions
449
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summation of floor function involving prime number

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#number-theory #prime-numbers #ceiling-and-floor-functions
217
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Find a necessary and sufficient condition

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#calculus #real-analysis #sequences-and-series #convergence-divergence #ceiling-and-floor-functions
295
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Closed form of $\int{\lfloor{x}\rfloor}dx$

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#calculus #integration #sequences-and-series #ceiling-and-floor-functions #polylogarithm
99
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Number of discontinuities of $\lfloor\sin ^{-1} x\rfloor+\lfloor\cos ^{-1} x\rfloor$

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#algebra-precalculus #limits #trigonometry #solution-verification #ceiling-and-floor-functions
274
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Show that $g(x)=[\frac1x]\sin x$ has a limit in $x=0$.

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#calculus #limits #ceiling-and-floor-functions

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