Question

Arăți ca 29 la 2001 de piata scrie cu o suma de trei pătrate perfecte

Answer 1

Salut,

$29^{2001}=29\cdot 29^{2000}=(4+9+16)\cdot (29^{1000})^2=(2^2+3^2+4^2)\cdot (29^{1000})^2=\\=2^2\cdot (29^{1000})^2+3^2\cdot (29^{1000})^2+4^2\cdot (29^{1000})^2=\\=(2\cdot 29^{1000})^2+(3\cdot29^{1000})^2+(4\cdot29^{1000})^2.$

Green eyes.