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A common factor of ( 52 7 379 + 47 3 379 527^{379} + 473^{379} )

and

( 52 7 166 47 3 166 527^{166} - 473^{166} ) is

9 7 I don't Know 6 10

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1 solution

Omkar Kulkarni
Jan 24, 2015

Notice the last digits of both the expressions. You must be familiar with patterns that we require here.

The last digits of 52 7 379 527^{379} and 47 3 379 473^{379} will be 3 3 and 7 7 respectively. Hence when added, the last digit of the sum will be 0 0 , which means that the sum is a multiple of 10 10 .

The last digits of 52 7 166 527^{166} and 47 3 166 473^{166} will be 9 9 . Hence when subtracted, the last digit of the difference will be 0 0 , which means that the difference is a multiple of 10 10 .

Hence the answer.

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