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Exponent Problem Under 2 min

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by wcheng57 » Sun May 23, 2010 3:59 pm
How do you solve this problem as quickly as possible? I spent too much time doing this problem. What's the time-efficient way? Thanks.

(2^2 -1)(2^2 +1)(2^4+1)(2^8+1) =

a) 2^16 -1

b) 2^16 +1

c) 2^32 -1

d) 2^128 -1

e) 2^16(2^16 -1)
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Source: — Problem Solving |

by ayankm » Sun May 23, 2010 4:41 pm
This problem utilises the formula (a+b)(a-b) = a^2 - b^2.

(2^2 -1)(2^2 +1)(2^4+1)(2^8+1)
= (2^4 - 1)(2^4 + 1)(2^8+1) --> because (2^2 -1)(2^2 +1) resembles the formula (a+b)(a-b) = a^2 - b^2
= (2^8 - 1)(2^8+1)
= 2^16 - 1.

Ans is Option A.
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by wcheng57 » Sun May 23, 2010 5:18 pm
Thanks. I knew there was a fundamental principle that was tested.
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