Question

Arătați ca 25 la puterea 2011 se poate scrie ca o suma de doua pătrate perfecte ! Ajutorrrr

Answer 1

$25 {}^{2011} = {25}^{2010 + 1} = {25}^{2010} \times 25 \\ = {25}^{2010} \times (16 + 9) \\ = {25}^{2010} \times 16 + {25}^{2010} \times 9 \\ = {25}^{1005 \times 2} \times 4 {}^{2} + {25}^{1005 \times 2} \times {3}^{2} \\ = ( {25}^{1005} \times 4) {}^{2} + ( {25}^{1005} \times 3) {}^{2}$