Explicație pas cu pas:
[tex]d = ( {4}^{50} + {4}^{49} + {4}^{48}) \div 21 = {4}^{48}( {4}^{50 - 48} + {4}^{49 - 48} + {4}^{48 - 48}) \div 21 = {4}^{48}( {4}^{2} + {4}^{1} + {4}^{0}) \div 21 = {4}^{48}(16 + 4 + 1) \div 21 = {4}^{48} \times 21 \div 21 = {4}^{48} [/tex]
[tex]d = {4}^{48} = {4}^{24 \times 2} = \left({4}^{24} \right)^{2} \\ [/tex]
→ d este pătrat perfect
[tex]{4}^{48} = {4}^{48} = {4}^{16 \times 3} = \left({4}^{16} \right)^{3} \\ [/tex]
→ d este cub perfect
