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Arartati ca n=2001+2(1+2+...+2000) este patrat perfect .

Răspuns :

2001+2(1+2000+2+1999+3+1998+...+1000+1001)=2001+2(1000·2001)=
=2001+2000·2001=2001(1+2000)=2001·2001=2001²