1) Fermat method of infinite descent
Fermat无穷递降法
1.
We use elementary theory of number and Fermat method of infinite descent,some necessary conditions if the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive integer solutions that fit (x,y) =1m.
利用Fermat无穷递降法 ,证明了方程x4 +mx2 y2 +ny4 =z2 在 (m ,n) =(± 18,5 4 ) ,(36 ,- 10 8) ,(± 36 ,10 8) ,(± 18,- 10 8) ,(- 18,10 8) ,(± 36 ,75 6 )时均无正整数解 ,并且获得了方程在 (m ,n) =(± 6 ,-2 4 ) ,(± 12 ,132 ) ,(- 36 ,- 10 8) ,(18,10 8)时无穷多组正整数解的通解公式 。
2.
We make use elementary theory of number and Fermat method of infinite descent,somenecessary conditions if the diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fir (x,y) =1
Fermat无穷递降法 ,证明了方程x4 +mx2 +ny4 =z2 =z2 在 (m ,n) =± (6,-3 3 ) ,(6,3 3 ) ,(-3 ,-6) ,(± 1 2 ,1 68) ,(-6,-1 2 ) ,(1 2 ,84)均无正整数解 ,并且获得了方程在 (-3 ,6) ,(6,-1 5 ) ,(± 3 ,-3 )时的无穷多组正整数解的通解公式 ,从而完善了Aubry等人的结
3.
With the help of the elementary theory of number and Fermat method of infinite descent,some necessary conditions have been proved provided that the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fit (x,y) =1 m.
利用数论方法及Fermat无穷递降法 ,证明了丢番图方程x4 +mx2 y2 +ny4 =z2 在 (m ,n) =(± 6,-3 ) ,(6,3 ) ,(± 3 ,3 ) ,(-12 ,2 4) ,(± 12 ,-2 4) ,(± 6,15 ) ,(-6,-15 ) ,(3 ,6)仅有平凡整数解 ,并且获得了方程在 (-6,3 ) ,(12 ,2 4) ,(3 ,-6) ,(-6,3 3 )时的无穷多组正整数解的通解公式 ,从而完善了Aubry等人的结
2) method of infinite descent
无穷递降法
1.
In this paper,we use Fermat method of infinite descent which shows that the Diophantine equations x 3±y 6=z 2 has no positive integer solutions when (x,y)=1 and y>1.
利用Fermat无穷递降法 ,证明了丢番图方程x3 ±y6=z2 ,(x ,y) =1仅有整数解 2 3 +16=32 。
3) Application of Infinite Successive Falling Method
无穷递降法的应用
4) Fermat's method of descent
Fermat下降法
5) infinite drop law
无穷下降法
1.
The square triangular number theorem is proved using the Ferma infinite drop law,thus explained the square triangular number existence infinite many this fact,and has given the square triangular number expression method.
利用F erm a的无穷下降法证明了平方三角数定理,从而说明了平方三角数存在无穷多个这一事实,并且给出了平方三角数的表示方法。
6) infinite decrease method
无限递降法
补充资料：递降
1.依次降低;逐渐降低。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条