Number Theory
Euler's Theorem
Is there a positive integer \(n\) such that \(2^n \equiv 1 \pmod{7} \, ?\)
\[\frac{1}{15}, \frac{2}{15}, \frac{3}{15}, \ldots, \frac{14}{15}, \frac{15}{15}\] How many of these fractions cannot be reduced?
Is 999999 divisible by 7?
Hint: \(999999 = 10^6 - 1.\)
What is the last digit of \(3^{100} \, ?\)
Which of these is congruent to \(10^{100} \pmod{11} \, ?\)