Cho $2.x^{4}=y^{4}+2017$
Cmr: $(x^{4}-y^{4})\vdots $8
Edited by lylymaymac, 11-06-2016 - 20:54.
Cho $2.x^{4}=y^{4}+2017$ Cmr: $(x^{4}-y^{4})\vdots $8
Started By lylymaymac, 11-06-2016 - 20:38
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Posted 11-06-2016 - 20:38
lylymaymac
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#2
Posted 11-06-2016 - 21:00
LuaMi
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Binh nhất
Cho $2.x^{4}=y^{4}+2017$
Cmr: $(x^{4}-y^{4})\vdots $8
Từ gt ta có $y$ lẻ$\Rightarrow y^4\equiv 1(mod 8)\Rightarrow y^4+2017\equiv 2(mod 8)\Rightarrow x^4\equiv 1(mod 8)\Rightarrow đpcm$
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