Question

Va rog cat mai repede a) Aratati ca A=1 + 5 la puterea a doua + 5 la puterea 4 +...+5 la puterea 34 este divizibil cu 26

Answer 1

$1+5^2=26 \\ \\ A=(1+5^2)+(5^4+5^6)+....+(5^{32}+5^{34}) \\ \\ =(1+5^2)+5^4(1+5^2)+...+5^{32}(1+5^2) \\ \\ =26+5^4\cdot26+...+5^{32}\cdot26 \\ \\ =26(1+5^4+...+5^{32})~\vdots~26$