Question

Aratati ca urmatoarele nr. sunt patrate perfecte:
a) 1+2+3+.... +1000+501 · 1001
b) 1+2+3+...+1011+505 · 1011

Answer 1

a) 1+2+3+.....+1000+501*1001=
    =1000*1001:2+501*1001=
    =500*1001+501*1001=
    =1001*(500+501)=
    =1001*1001=1001²⇒ p.p

b)  1+2+3+...+1011+505*1011=
     =1011*1012:2+505*1011=
     =1011*506+505*1011=
     =1011*(506+505)=
     =1011*1011=1011²⇒ p.p