@article{Cheenchan_2016, title={On the diophantine equation px+5y=z2}, volume={8}, url={https://ph01.tci-thaijo.org/index.php/snru_journal/article/view/55337}, abstractNote={<span>The aim of this work is to show that the Diophantine equations <span><em>p z </em><span><em>x y </em><span>  <span>5 <span>2 <span>where <span><em>p </em><span>is prime number <span>and <span><em>p </em><span>satisfies; case 1: <span><em>p </em><span><span>1 (mod 4) <span>or case 2: <span><em>p </em><span> <span>3 (mod4) <span>and <span><em>p </em><span> <span>2 (mod5) <span>or case 3: <span><em>p </em><span> <span>3 (mod4) <span>and <span><em>p </em><span> <span>3 (mod5) <span>, has no non-negative integer solution. In addition, the Diophantine<br /><span>equations <span><em>p z </em><span><em>x y </em><span>  <span>5 <span>2 <span>have some non-negative integer solutions (<span><em>p, x, y, z</em><span>) if <span><em>p </em><span> <span>3(mod 4) <span>and <span><em>p </em><span><span>1(mod5) <span>, such as (11, 1, 2, 6), (11, 1, 1, 4), (31, 1, 1, 6), (71, 1, 3, 4), (131, 1, 3, 16) and (191, 1, 1, 14), etc.<br /><span>Moreover, if <span><em>p </em><span> <span>3(mod 4) <span>and <span><em>p </em><span> <span>4(mod5)<span>, such as (19, 1, 3, 12), (139, 1, 1, 12) and (199, 1, 3, 18).</span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>}, number={1}, journal={Creative Science}, author={Cheenchan, I-lada}, year={2016}, month={Apr.}, pages={146–148} }