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On the Solutions of the Diophantine Equation ua+vb=z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u ^a + v^b=z^2$$\ end{document} for Some Prime Pairs u and v
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On the Exponential Diophantine Equation px+qy=z3:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p^x+q^y=z^3: $$\ end{document} Theorems and Conjectures
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