MathDB

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Part of 2004 Nicolae Coculescu

Problems(4)

Simple eq. |x-1|+|x-a|+|x-b|=1

Source:

12/14/2019
Find all pairs of integers (a,b) (a,b) such that the equation ∣x−1∣+∣x−a∣+∣x−b∣=1 |x-1|+|x-a|+|x-b|=1 has exactly one real solution.
Florian Dumitrel
equationsalgebra
x²+7^x=y³,x²+3=2^y (system)

Source:

12/14/2019
Solve in the real numbers the system: {x2+7x=y3x2+3=2y \left\{ \begin{matrix} x^2+7^x=y^3\\x^2+3=2^y \end{matrix} \right.
Eduard Buzdugan
equationsystem of equationsmonotonyalgebra
Limit involving the harmonic sequence as exponent

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12/14/2019
Calculate lim⁡n→∞(e1+1/2+1/3+⋯+1/n+1/(n+1)−e1+1/2+1/3+⋯+1/n). \lim_{n\to\infty } \left( e^{1+1/2+1/3+\cdots +1/n+1/(n+1)} -e^{1+1/2+1/3+\cdots +1/n} \right) .
Sequencesserieslimitsharmonic seriescalculus
a,b s.t. a³b=ba²,a²b=ba³ in group

Source:

12/14/2019
Let b,a b,a be two elements of a group chosen such that a3b=ba2 a^3b=ba^2 and a2b=ba3. a^2b=ba^3. Prove that the order of a a divides 5. 5.
Gabriel Tica
group theory