Question

Scrieti numarul 29 la puterea 2001 ca o suma de 3 patrate perfecte

Answer 1

   
[tex]\displaystyle\\ 29^{2001}=29^{2000+1}=29^{2000}\times29^1=29\times29^{1000\times2} =\\\\ =(16+4+9)\times\Big(29^{1000}\Big)^2}=(4^2+2^2+ 3^2)\times\Big(29^{1000}\Big)^2}=\\\\ = 4^2\times\Big(29^{1000}\Big)^2}+2^2\times\Big(29^{1000}\Big)^2}+3^2\times\Big(29^{1000}\Big)^2}=\\\\ =\underbrace{\Big(4\times29^{1000}\Big)^2}}_{\text{\bf Patrat perfect}}+\underbrace{\Big(2\times29^{1000}\Big)^2}}_{\text{\bf Patrat perfect}}+\underbrace{\Big(3\times29^{1000}\Big)^2}}_{\text{\bf Patrat perfect}}[/tex]