5(power 2009) + 13(power 2009). divide it by 18.

Asked by Lochan Khatri | 19th Apr, 2013, 03:33: PM

Expert Answer:

The remainder on dividing 5(power 2009) + 13(power 2009) by 18 is 0.
 
Here is the explanation-
 
1) 13^2009 = (18-5)^2009

2) Using Binomial expansion (18-5)^2009 = 

= 18^2009 + C?(18^2008)(-5) + C?(18^2007)(-5)² + C?(18^2006)(-5)³ + ------ + (-5)^2009

3) In the above all the terms except last one is divisible by 18; 
hence the remainder is (-5)^2009 = -(5^2009)

4) As such the remainder in 13^2009 + 5^2009, 
when divided by 18 is {-(5^2009) + (5^2009)} = 0

Thus the remainder is zero.

Answered by  | 19th Apr, 2013, 06:59: PM

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