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Question-201956




Question Number 201956 by sonukgindia last updated on 16/Dec/23
Commented by mahdipoor last updated on 16/Dec/23
5^2^(117)  −1=(5^2^(116)  −1)(5^2^(116)  +1)=  (5^2^(115)  −1)(5^2^(115)  +1)(5^2^(116)  +1)=  ...  =(5^2^1  −1)(5^2^1  +1)...(5^2^(116)  −1)
$$\mathrm{5}^{\mathrm{2}^{\mathrm{117}} } −\mathrm{1}=\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } −\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } +\mathrm{1}\right)= \\ $$$$\left(\mathrm{5}^{\mathrm{2}^{\mathrm{115}} } −\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{\mathrm{115}} } +\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } +\mathrm{1}\right)= \\ $$$$… \\ $$$$=\left(\mathrm{5}^{\mathrm{2}^{\mathrm{1}} } −\mathrm{1}\right)\left(\mathrm{5}^{\mathrm{2}^{\mathrm{1}} } +\mathrm{1}\right)…\left(\mathrm{5}^{\mathrm{2}^{\mathrm{116}} } −\mathrm{1}\right) \\ $$
Answered by AST last updated on 16/Dec/23
(5^2 −1)P=1⇒P=(1/(24))
$$\left(\mathrm{5}^{\mathrm{2}} −\mathrm{1}\right){P}=\mathrm{1}\Rightarrow{P}=\frac{\mathrm{1}}{\mathrm{24}} \\ $$
Commented by Frix last updated on 17/Dec/23
Yes!
$$\mathrm{Yes}! \\ $$

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