Geodesic
On the Diophantine equation xx⋅yyk(y)=zzp
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 121-124.

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In this paper the existence and the ways of finding some positive integer solutions x,y,z for the equation xx⋅yyk(y)=zzp are studied. 
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     title = {On the {Diophantine} equation $x^x\cdot y^{y^{k(y)}}=z^{z^p}$},
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Gheorghe M. Tudor; Tudor Bînzar. On the Diophantine equation $x^x\cdot y^{y^{k(y)}}=z^{z^p}$. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 121-124. https://geodesic-test.mathdoc.fr/item/BASM_2010_2_a8/

[1] Andreescu T., Andrica D., An Introduction to Diophantine Equations, Gil Publishing House, 2002 | Zbl

[2] Mordell L. J., Diophantine Equations, Academic Press, London–New York, 1969 | MR | Zbl

[3] Sierpinski W., What we know and what we don't know about prime numbers, Bucharest, 1966 (in Romanian) | MR

[4] Tudor Gh. M., “L'équation Diophantienne $x_1^{x_1}\cdot x_2^{x_2}\cdot\ldots\cdot x_k^{x_k}=y_k^{y_k}$ (I)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 48(62):2 (2003), 13–18 | MR | Zbl

[5] Tudor Gh. M., “L'équation Diophantienne $(x_1^{x_1})^{m_1}\cdot(x_2^{x_2})^{m_2}\cdot\ldots\cdot(x_k^{x_k})^{m_k}=y_k^{y_k}$ (II)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 49(63):1 (2004), 13–19 | MR | Zbl

[6] Tudor Gh. M., “L'équation Diophantienne $x_1^{x_1}\cdot x_2^{x_2}\cdot\ldots\cdot x_k^{x_k}=y_1^{y_1}\cdot y_2^{y_2}\cdot\ldots\cdot y_k^{y_k}$ (III)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 49(63):2 (2004), 1–8 | MR | Zbl

[7] Tudor Gh. M., “L'équation Diophantienne $x_1^{x_1}\cdot x_2^{x_2}\cdot\ldots\cdot x_k^{x_k}=w^{w^p}$ (IV)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 50(64):1 (2005), 12–18 | MR | Zbl

[8] Tudor Gh. M., “L'équation Diophantienne $x^{x}\cdot y^{y^q}=z^{z^p}$ (V)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 50(64):2 (2005), 18–24 | MR

[9] Tudor Gh. M., Bînzar T., “On some exponential Diophantine equations”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 50(64):2 (2005), 47–52 | MR | Zbl

[10] Tudor Gh. M., Bînzar T., “On the Diophantine equation $x_1^{x_2^\alpha}\cdot x_2^{x_3^\alpha}\cdot\ldots\cdot x_k^{x_1^\alpha}=w^{w^\alpha}$, $\alpha=\pm1$ (II)”, Bul. Şt. al Univ. “Politehnica” din Timişoara, Seria Mat.-Fiz., 53(67):1 (2008), 44–49 | MR | Zbl