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## On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$

#### SALAH EDDINE RIHANE [1] , BERNADETTE FAYE [2] , FLORIAN LUCA [3] , ALAIN TOGBE [4]

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In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.
Pell numbers, linear form in logarithms, reduction method
Journal Section Articles Author: SALAH EDDINE RIHANE Author: BERNADETTE FAYE Author: FLORIAN LUCA Author: ALAIN TOGBE
 Bibtex @ { tbtkmath575372, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {TUBITAK}, year = {2019}, volume = {43}, pages = {1640 - 1649}, doi = {}, title = {On the exponential Diophantine equation \$P\_n\^x+P\_\{n+1\}\^x=P\_m\$}, key = {cite}, author = {RIHANE, SALAH EDDINE and FAYE, BERNADETTE and LUCA, FLORIAN and TOGBE, ALAIN} } APA RIHANE, S , FAYE, B , LUCA, F , TOGBE, A . (2019). On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$. Turkish Journal of Mathematics, 43 (3), 1640-1649. Retrieved from http://dergipark.org.tr/tbtkmath/issue/45655/575372 MLA RIHANE, S , FAYE, B , LUCA, F , TOGBE, A . "On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$". Turkish Journal of Mathematics 43 (2019): 1640-1649 Chicago RIHANE, S , FAYE, B , LUCA, F , TOGBE, A . "On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$". Turkish Journal of Mathematics 43 (2019): 1640-1649 RIS TY - JOUR T1 - On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$ AU - SALAH EDDINE RIHANE , BERNADETTE FAYE , FLORIAN LUCA , ALAIN TOGBE Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 1640 EP - 1649 VL - 43 IS - 3 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2019 ER - EndNote %0 Turkish Journal of Mathematics On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$ %A SALAH EDDINE RIHANE , BERNADETTE FAYE , FLORIAN LUCA , ALAIN TOGBE %T On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$ %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 3 %R %U ISNAD RIHANE, SALAH EDDINE , FAYE, BERNADETTE , LUCA, FLORIAN , TOGBE, ALAIN . "On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$". Turkish Journal of Mathematics 43 / 3 (June 2019): 1640-1649.