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设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q,证明1979|p
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设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q,证明1979|p
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设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q(最简分数),证明1979|p
p/q=1+1/2+1/3+1/4+.+1/1319- 2(1/2+1/4+1/6+...+1/1318)
=1+1/2+1/3+1/4+.+1/1319- (1+1/2+1/3+...+1/659)
=1/660+1/661+1/662+.+1/1318+1/1319 (660项)
=(1/660+1/1319)+(1/661+1/1318)+...+(1/329+1/330) (330组)
=1979/(660*1319)+1979/(661*1318)+...+1979/(329*330)
=1979*(1/660*1319 +1/661*1318+...+1/329*330)=1979*m/n (设m/n最简分数)
=> n=q ;1979m=p =>1979|p
p/q=1+1/2+1/3+1/4+.+1/1319- 2(1/2+1/4+1/6+...+1/1318)
=1+1/2+1/3+1/4+.+1/1319- (1+1/2+1/3+...+1/659)
=1/660+1/661+1/662+.+1/1318+1/1319 (660项)
=(1/660+1/1319)+(1/661+1/1318)+...+(1/329+1/330) (330组)
=1979/(660*1319)+1979/(661*1318)+...+1979/(329*330)
=1979*(1/660*1319 +1/661*1318+...+1/329*330)=1979*m/n (设m/n最简分数)
=> n=q ;1979m=p =>1979|p
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