关于丢番图方程x^4-4x^2y^2+y^4=193

On Diophantine Equation x^4- 4x^2y^2 +y^4 =193

证明了丢番图方程ｘ４－４ｘ２ｙ２＋ｙ４＝１９３仅有正整数解（ｘ， ｙ＝（１，４）和（４，１），进而又推得丢番图方程 ｘ４－ １０ｘ２ｙ２＋ｙ４＝－１５４４仅有正整数解（ｘ，ｙ ）＝（ ３， ５）和（５， ３）．

In the paper, the following theorem is proved. Theorem The diophantine equation x4- 4x2y2+y4=193 has only positive integer solutions (x, y)= (l, 4) and (4, l).