n=50k; n∈N*
A={1;2;3;…….;n}
Suma elementelor mulțimii A:
1+2+3+……+n=n(n+1)/2=50k(50k+1)/2=25k(50k+1)
suma multiplilor lui 50=
=50•1+50•2+…..+50k
=50(1+2+…+k)=50•k•(k+1)/2=25k(k+1)
=> 25k(50k+1)- 25k(k+1)
=25k(50k+1-k-1)
=25k•49k
=(5•7•k)²
=(35k)² este patrat perfect
