Number Theory
# Euler's Theorem

Is there a positive integer $n$ such that $2^n \equiv 1 \pmod{7} \, ?$

**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 $10^{100} \pmod{11} \, ?$