设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q,证明1979|p

问题描述:

设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q,证明1979|p

设1-1/2+1/3-1/4+.-1/1318+1/1319=p/q(最简分数),证明1979|pp/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...