Fermat's little theorem and congruence equations Quiz

1. By Fermat's little theorem, $2^{10}\equiv$ what, modulo $11$?

• A. $1$
• B. $2$
• C. $10$
• D. $0$

2. What is $3^{50}$ modulo $7$?

• A. $1$
• B. $3$
• C. $2$
• D. $4$

3. What is the multiplicative inverse of $5$ modulo $7$?

• A. $2$
• B. $3$
• C. $4$
• D. $5$

4. Which congruence has no solutions?

• A. $4x\equiv2\pmod6$
• B. $9x\equiv6\pmod{12}$
• C. $5x\equiv1\pmod8$
• D. $8x\equiv5\pmod{12}$

5. How many solutions modulo $12$ does $8x\equiv4\pmod{12}$ have?

• A. $4$
• B. $1$
• C. $2$
• D. $8$