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發表 tangpakchiu 於 星期日 七月 02, 2006 6:11 pm

#ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#試證明四個連續奇數的乘積加上16必為一個整數的平方 #ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl##ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#一個差不多的解法:#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#(2n-3)(2n-1)(2n+1)(2n+3)+16#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#=(4n^2-9)(4n^2-1)+16#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#令y=4n^2-1#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#y^2-8y+16#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl#=(y-4)^2#ed_op#/FONT#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl#

發表 lcflcflcf 於 星期日 七月 02, 2006 5:46 pm

四個連續奇數的乘積加上16
=(2n+1)(2n+3)(2n+5)(2n+7)+16
=16n^4+128n^3+334n^2+352n+121
=(4n^2+16n+11)^2

[數學]數學題..(88)

發表 ☆ ~ 幻 星 ~ ☆ 於 星期日 七月 02, 2006 4:07 pm

試證明四個連續奇數的乘積加上16必為一個整數的平方