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This work determine the entire family of positive integer solutions of the diophantine equation. The solution is described in terms of $frac{(m-1)(m+n-2)}{2} $ or $frac{(m-1)(m+n-1)}{2}$ positive parameters depending on $n$ even or odd. We find the solution of a diophantine system of equations by using the solution of the diophantine equation. We generalized all the results of the paper [5].
Suppose that $n$ is a positive integer. In this paper, we show that the exponential Diophantine equation $$(n-1)^{x}+(n+2)^{y}=n^{z}, ngeq 2, xyz eq 0$$ has only the positive integer solutions $(n,x,y,z)=(3,2,1,2), (3,1,2,3)$. The main tools on the p
We explore the utility of CI as an alternative high-fidelity gas mass tracer for Galactic molecular clouds. We evaluate the X$_{rm CI}$-factor for the 609 $mu$m carbon line, the analog of the CO X-factor, which is the ratio of the H$_2$ column densit
We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-bar{D}^*$ molecular currents. We found (within our approximati
We show that in the Standard Model the parametrically leading (by a factor 1/alpha_s) contribution to the inclusive CP asymmetry in B->X_{s,d}+gamma decays arises from a long-distance effect in the interference of the electromagnetic dipole amplitude
Lately, the LHCb Collaboration reported the discovery of two new states in the $B^+rightarrow D^+D^- K^+$ decay, i.e., $X_0(2866)$ and $X_1(2904)$. In the present work, we study whether these states can be understood as $D^*bar{K}^*$ molecules from t