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Is there a positive integer nnn such that 2n≡1(mod7) ?2^n \equiv 1 \pmod{7} \, ?2n≡1(mod7)?
115,215,315,…,1415,1515\frac{1}{15}, \frac{2}{15}, \frac{3}{15}, \ldots, \frac{14}{15}, \frac{15}{15}151,152,153,…,1514,1515 How many of these fractions cannot be reduced?
Is 999999 divisible by 7?
Hint: 999999=106−1.999999 = 10^6 - 1.999999=106−1.
What is the last digit of 3100 ?3^{100} \, ?3100?
Which of these is congruent to 10100(mod11) ?10^{100} \pmod{11} \, ?10100(mod11)?
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