Răspuns:
Explicație pas cu pas:
Progresie geometrica cu ratia q=3 b1=3 n=60
S=b1⋅(q^n-1)/(q-1)=3×(3^60-1)/(3-1)=3(3^30-1)(3^30+1)/2=
=3(3^15-1)(3^15+1)(3^30+1)/2=3(3^5-1)(3^10+3^5+1)(3^5+1)(3^10-3^5+1)(3^30-1)(3^30+1)/2=3×242×244×(3^10+3^5+1)(3^10-3^5+1)(3^30-1)(3^30+1)/2=
=3×242×244×59296×(3^10-3^5+1)(3^30-1)(3^30+1)/2=3×242×244×4561×13×
×(3^10-3^5+1)(3^30-1)(3^30+1)/2=3×121×244×4561×52×(3^10-3^5+1)(3^30-1)(3^30+1)/2
3^5=243 rezultatul se divide cu 2, cu 3,cu 4, cu 13 ⇒ se divide si cu 52!
am folosit a²-b²=(a-b)(a+b) si a³+-b³=(a+-b)(a²+-ab+b³)
