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Find the solution of $x^2-4=[x]$

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#algebra-precalculus #ceiling-and-floor-functions #fractional-part
88
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Evaluating a Double Integral Involving Fractional Part Functions

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#multivariable-calculus #multiple-integral #fractional-part
120
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Average Number of Small Divisors

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#number-theory #analytic-number-theory #divisor-sum #fractional-part #divisor-counting-function
144
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How can I prove that $a_n>0$ infinitely often?

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#functions #trigonometry #factorial #pi #fractional-part
27
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Dividing an interval into sections (fractional)

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#inequality #fractional-part
880
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Domain of $f(x)=1/\sqrt{\left\{x+1\right\}-x^2+2x}$ where {.} denotes the fractional part of $x$.

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#functions #fractional-part
404
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Summation of square root fractional part

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#number-theory #summation #fractional-part
144
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Prove that $(3/2)^n\bmod 1\equiv (2^n-1)/2^n $ has infinitely many solutions as $n \to\infty$

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#limits #number-theory #algebraic-number-theory #fractional-part #modular-function
49
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Better way to compute this definite piecewise integral

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#definite-integrals #ceiling-and-floor-functions #riemann-sum #fractional-part
90
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Number theory Question From RMO(2015) regarding fractional part function.

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#elementary-number-theory #algebraic-number-theory #ceiling-and-floor-functions #fractional-part
85
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$\{a\}+\{1/a\}=1$ prove that $\{a^3\}+\{1/a^3\}=1$

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#algebra-precalculus #fractional-part
100
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If $\{x\}$ denotes the fractional part of x, then what is $\{\dfrac{3^{2n}}{8}\}$, where n $\in$ N

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#binomial-theorem #fractional-part
241
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$\{x^2\} = \{x\}^2$, how many solutions in interval $[1, 10]$

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#graphing-functions #integers #ceiling-and-floor-functions #fractional-part
150
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How do we solve $x^2 + \{x\}^2 = 33$ without computer?

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#algebra-precalculus #ceiling-and-floor-functions #fractional-part
154
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Fractional part sequence

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#real-analysis #calculus #sequences-and-series #arithmetic #fractional-part

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