Edited by Hoang Huy Thong, 04-10-2012 - 20:40.
Chứng minh $ab(a^{2}-b^{2})\vdots 3$
#1
Posted 04-10-2012 - 19:24
#2
Posted 04-10-2012 - 19:43
#3
Posted 04-10-2012 - 20:42
Nếu a,b cùng tính chẵn lẻ thì $a^2-b^2$ chia hết cho 2.Chứng minh $ab(a^{2}-b^{2})\vdots 3$
Nếu a,b khác tính chẵn lẻ thì 1 trong 2 số là chẵn nên ab chia hết cho 2
1 số chính phương chia 3 dư 0 hoặc 1.Nếu $a^2,b^2$ đồng dư thì $a^2-b^2$ chia hết cho 3.Nếu $a^2;b^2$ ko đồng dư thì ít nhất 1 trong 2 số chia hết cho 3 nên $ab$ chia hết cho 3.
Từ đó ta có đpcm.
#4
Posted 06-10-2012 - 12:08
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#5
Posted 06-10-2012 - 12:36
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