Question

Arătați ca 16 la puterea 5 + 2 la puterea 15 e divizibil cu 33

Answer 1

16⁵ + 2¹⁵ = 

= 2⁴⁾⁵ + 2¹⁵

= 2²⁰ + 2¹⁵

= 2¹⁵ ·(2⁵ + 1)

= 2¹⁵·(32 + 1)

= 2¹⁵·33 divizibil cu 33

Answer 2

$16^{5}+2^{15}=\\ \\=(2^{4})^{5}+2^{15}=\\ \\=2^{4*5}+2^{15}=\\ \\=2^{20}+2^{15}=\\ \\=2^{15}(2^{5}+1)=\\ \\=2^{15}(32+1)=\\ \\=2^{15}*33~divizibil~cu~33\\ \\ \rightarrow~16^{5}+2^{15}~este~divizibil~cu~33$