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5 2009 +13 2009 ÷8 Find the remainder Please tell the process

52009+132009÷8 
Find the remainder 
Please tell the process
 

Grade:10

2 Answers

Arun
25763 Points
2 years ago
Here, we have 5^2009 + 13^2009

We know that a^n + b^n is always divisible by (a+b) when n is odd.

2009 is an odd number.
So, 5^2009 + 13^2009 is divisible by (5+13) i.e 18.

Hence, the remainder is 0.
Aditya Gupta
2075 Points
2 years ago
Actually 5^2009= 5*25^1004 
Note that 25=8*3+1
Since remainder of 25^n when divided by 8 is 1, so remainder when 5^2009 divided by 8 is 5
Now 13^2009=13*169^1004
But 169= 8*21+1
So remainder when 13^2009 is divided by 8 is 13*1 or 13-8= 5
So net remainder is 5+5=10 or 10-8 
=2

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