Clearly A A a b 1 1 a b 1 H H G G A A H H H H Also 3ab 1 1 1 1 1 4 2006 H H 2a b and 2 1 3 b A A H H H H a b A A H H ab G G 1 3ab a b 3ab 2a a 1 2b a 2a b 2b a 2a b 9ab Let P n 25 1 24 n 5735 For n 1 P 1 625 24 5735 6336 24 x 11 which is divisible by 242 Hence P 1 Is true Let P K be the true where K 2 1 25 1 24 K 5735 24 2 where AEN For n k 1 P K 1 25 2 24 K 5735 25 25 1 24 K 5735 25 24 K 25 5735 5735 24 K 1 25 24 2 24 2K 5735 24 24 25 24 24 2 K 24 5736 25 24 24 K 24 239 24 25 K 230 which is divisible by 24 2 Hence by the method of mathematical Induction result is true vne N
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