anonymous
  • anonymous
What is the remainder when 2 to the power of 2009 and 2009 squared are added together and divided by 13?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
The answer is 3. Do you need a mathematical explanation?
anonymous
  • anonymous
I think I need an explanation.
anonymous
  • anonymous
hang on a sec

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anonymous
  • anonymous
2009^2 will have the last 2 digits 81. 2^n will have last digit: 2 if n mod 4 = 1 4 if n mod 4 = 2 6 if n mod 4 = 3 8 if n mod 4 = 0 2009 mod 4 = 1 so the last digit will be 2 (......2 + .....1) = ...... 3 (.....3) mod 13 could possibly be 3 This is not definitely true though, if (the number was ....13) for example, then the answer would be 0. You would have to look into the patterns of the last 2 digits of 2^n. There is a pattern I can tell you that. From the pattern you could tell if it would be 3 or 0. However, I just put it into wolframalpha.com to get the result of 3
anonymous
  • anonymous
Actually I am wrong. It depends on much more than the first two numbers, because you are dividing by 13. So I don't have an explanation on this one. Sorry

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