Question

Aratati ca 100 la puterea 2013 se poate scrie ca o suma de doua patrate perfecte

Answer 1

${100}^{2013} = 100 \times {100}^{2012} = (64 + 36) \times {100}^{2012} = \\ ( {8}^{2} + {6}^{2}) \times ({100}^{1006}) ^{2} = {8}^{2} \times ( {100}^{1006} ) ^{2} + {6}^{2} \times ( {100}^{1006} ) ^{2} = \\ (8 \times {100}^{1006} )^{2} + (6 \times {100}^{1006} )^{2}$