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Aratati ca numarul n=145+2·(1+2+....+144) este patrat perfect.

Răspuns :

=145+2(144x(144+1):2)=145+(144x145)=145(1+144)=145x145
1+2+.........+144=(1+144).144/2
n=145+2.145.144/2
n=145+145.144=145.145
n=145²