Question

2^6n divide paranteză rotundă la 8^2n +1 + 4^3n+1-11×64^n

Answer 1

$8^{2n+1}+4^{3n+1}-11*64^n= \\\\= 2^{3(2n+1)}+2^{2(3n+1)}-11*2^{6n}= \\\\= 2^{6n+3}+2^{6n+2}-11*2^{6n}= \\\\= 2^3 * 2^{6n}+ 2^2* 2^{6n}-11*2^{6n}= \\\\= 2^{6n}(8+4-11)= \\\\= 2^{6n}*(12-11)= \\\\= 2^{6n} \ \ \ \vdots \ \ \ 2^{6n} \ \ \ c.c.t.d.$