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Question Number 140606 by mathsuji last updated on 10/May/21
(1+x)2023(1−x+x2)2022=a0+a1x+a2x2+...+a6067x6067alsoiftheequationsan≡1(mod5),an≡2(mod5),n=0;1;2;...;6067hasuandvsolutionsrespectivley,thenprovethat...1+21+31+41+...=1+u⋅v
Commented by mathsuji last updated on 10/May/21
Sirmr.Wpliz...
Commented by mr W last updated on 10/May/21
1+21+31+41+...=3an=Ck2022withn=3k,k=0,1,..,2022an=Ck2022withn=3k+1wehave4timesanwithan≡1mod5,i.e.2timesC02022and2timesC22022.wehave2timesanwithan≡2mod5,i.e.2timesC12022.thatmeansu=4,v=21+uv=1+4×2=3
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