Difference between revisions of "1972 AHSME Problems/Problem 31"
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When the number <math>2^{1000}</math> is divided by <math>13</math>, the remainder in the division is | When the number <math>2^{1000}</math> is divided by <math>13</math>, the remainder in the division is | ||
Revision as of 14:05, 23 June 2021
Problem
When the number is divided by
, the remainder in the division is
Solution
By Fermat's little theorem, we know that . However, we find that
, so
, so the answer is
.