[]2̵Ǥ뤳Ȥ
[]ǰʬΰȤäƾΤ̡
[̾]2̵Ǥ뤳ȤˤϡʤȤФ褤
x2=2y2(*)
ʤʤСx,y(*)Ȥx/y=2ΩĤȤƱǤ뤫Ǥ롣
Ǥ2ˡȤƹͤ롣2ˡȤơx,yΤ٤ƤȤ߹碌ˤơ2ˡȤx22y{2};ͤȡɽ롣
x | y | x2 | 2y2 | |
0 | 0 | 0 | 0 | |
0 | 1 | 0 | 0 | |
1 | 0 | 1 | 0 | |
1 | 1 | 1 | 0 |
x22y2 (mod 2)ΩʤȤˡߤ
ȡxξ硢¨x1 (mod 2)ξ硢ߤˤʤäƤ롣Ĥޤꡢ(*)x϶ǤʤФʤʤǡx=2x1(x1)֤
(*)ȡ22x12=2y2Ȥʤ롣
2x12=y2
(*)x,y줾y,x1֤ΤƱǤ롣
ǡyФƾ嵭ƱȡyǤʤФʤʤ
äơy=2y1(y1)֤ơ22y12=2x12Ȥʤ롣Ĥޤꡢx12=2y12Ǥ뤬Ϥޤ(*)ƱƤΤǡ嵭ƱŬѤǤ롣
Τ褦ˡƱ֤ȡxy2dzʤƤϤʤʤȤˤʤ롣ԲǽǤ롣
(*)˼Ȥ̷꤫⤬ƳʤäΤǡ¸ߤʤȤ줿