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Question Number 218400 Answers: 4 Comments: 0

Hard problem..... prove. for all α∈Z α^(37) ≡α Mod(1729) pls help :(

$$\mathrm{Hard}\:\mathrm{problem}..... \\ $$$$\:\mathrm{prove}. \\ $$$$\:\mathrm{for}\:\mathrm{all}\:\alpha\in\mathbb{Z} \\ $$$$\alpha^{\mathrm{37}} \equiv\alpha\:\mathrm{Mod}\left(\mathrm{1729}\right) \\ $$$$\mathrm{pls}\:\mathrm{help}\::\left(\right. \\ $$

Question Number 218399 Answers: 1 Comments: 0

Question Number 218398 Answers: 1 Comments: 0

Question Number 218397 Answers: 0 Comments: 0

Question Number 218396 Answers: 0 Comments: 0

Question Number 218395 Answers: 0 Comments: 0

Question Number 218393 Answers: 1 Comments: 0

let ABC be a triangle with incenter I. prove that Ia . Ib . Ic ≤ ((abc)/8)

$$ \\ $$$$\:{let}\:{ABC}\:{be}\:{a}\:{triangle}\:{with}\:{incenter}\:{I}. \\ $$$$\:{prove}\:{that}\:{Ia}\:.\:{Ib}\:.\:{Ic}\:\:\leqslant\:\frac{{abc}}{\mathrm{8}}\:\: \\ $$$$ \\ $$

Question Number 218383 Answers: 0 Comments: 2

Question Number 218385 Answers: 3 Comments: 0

Question Number 218384 Answers: 3 Comments: 0

Question Number 218388 Answers: 0 Comments: 0

Question Number 218376 Answers: 0 Comments: 0

∫_0 ^∞ ((J_𝛂 (ar))/((r^2 +k^2 )𝛍))dr

$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{J}}_{\boldsymbol{\alpha}} \left(\boldsymbol{{ar}}\right)}{\left(\boldsymbol{{r}}^{\mathrm{2}} +\boldsymbol{{k}}^{\mathrm{2}} \right)\boldsymbol{\mu}}\boldsymbol{{dr}}\: \\ $$$$ \\ $$

Question Number 218375 Answers: 1 Comments: 0

∫((√(tan x))/(sin^3 x cos x))dx

$$ \\ $$$$\:\:\int\frac{\sqrt{\boldsymbol{{tan}}\:\boldsymbol{{x}}}}{\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}\:\boldsymbol{{cos}}\:\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$$$ \\ $$

Question Number 218374 Answers: 0 Comments: 0

∫_0 ^∞ J_α ((√(ar)))e^(−r) dr

$$\: \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \boldsymbol{{J}}_{\alpha} \left(\sqrt{\boldsymbol{{ar}}}\right)\boldsymbol{{e}}^{−\boldsymbol{{r}}} \boldsymbol{{dr}}\: \\ $$$$\: \\ $$

Question Number 218366 Answers: 0 Comments: 2

Question Number 218365 Answers: 1 Comments: 0

Find: 𝛀 =lim_(n→∞) Σ_(k=1) ^n [ Σ_(i=1) ^k i (k − i + (1/3))]^(−1) = ?

$$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left[\:\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{k}}} {\sum}}\:\mathrm{i}\:\left(\mathrm{k}\:−\:\mathrm{i}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\right)\right]^{−\mathrm{1}} =\:? \\ $$

Question Number 218364 Answers: 1 Comments: 0

Let 𝛌>0 fixed Solve for real numbers the system: { ((x^2 − yz = λ^2 )),((y^2 − zx = 7λ^2 )),((z^2 − xy = −5λ^2 )) :}

$$\mathrm{Let}\:\:\:\boldsymbol{\lambda}>\mathrm{0}\:\:\:\mathrm{fixed} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{the}\:\mathrm{system}:\:\:\:\begin{cases}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{yz}\:=\:\lambda^{\mathrm{2}} }\\{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{zx}\:=\:\mathrm{7}\lambda^{\mathrm{2}} }\\{\mathrm{z}^{\mathrm{2}} \:−\:\mathrm{xy}\:=\:−\mathrm{5}\lambda^{\mathrm{2}} }\end{cases} \\ $$

Question Number 218358 Answers: 0 Comments: 0

Question Number 218356 Answers: 3 Comments: 0

Question Number 218357 Answers: 3 Comments: 0

Question Number 218345 Answers: 1 Comments: 0

Question Number 218344 Answers: 0 Comments: 1

Question Number 218349 Answers: 3 Comments: 0

Question Number 218354 Answers: 0 Comments: 0

Question Number 218331 Answers: 1 Comments: 0

∫_0 ^∞ ((x^2 sin (x))/(1+x^4 )) dx = ?

$$\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:=\:? \\ $$

Question Number 218328 Answers: 1 Comments: 0

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