Question

Sa se arate ca sumaS=1+5+5 la puterea doua+...5la puterea 1288+5 la puterea 1289 se divide cu 31

Answer 1

 [tex]Observam\;ca\;1+5+5^2=31\;\\ \rightarrow\;\;S=(1+5+5^2)+5^3(1+5+5^2)+...+5^{1287}(1+5+5^2)=\\ =31\cdot(1+5^3+...+5^{1287})\;\vdots\;31[/tex]

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