Find-the-factor-of-3-200-4-

Question Number 8026 by Nayon last updated on 28/Sep/16

F i n d t h e f a c t o r o f (3^{200} + 4)

Answered by Rasheed Soomro last updated on 28/Sep/16

3^{200} + 4

= {(3^{100})}^{2} + 2^{2}

= {(3^{100})}^{2} + 2 (3^{100}) (2) + 2^{2} - 2 (3^{100}) (2)

= {(3^{100} + 2)}^{2} - {(2 . 3^{50})}^{2}

= (3^{100} + 2 - 2 . 3^{50}) (3^{100} + 2 + 2 . 3^{50})

= (3^{100} - 2 . 3^{50} + 2) (3^{100} + 2 . 3^{50} + 2)