Question

Arătați ca nr c=(2la puterea 40+2la puterea 39+2la puterea 38):7 este pătrat perfect

Answer 1

$( 2^{40} +2^3^9+ 2^{38}):7=p.p \\ \\ 2^3^8*(1+2^1+2^2):7= \\ \\ 2^3^8*(1+2+4):7= \\ \\ 2^3^8*7:7= \\ \\ 2^3^8:1 \\ \\ 2^3^8=(2^1^9)^2 \\ \\ (2^1^9)^2:1=(2^1^9)^2=p.p$