February+14

Question 1

Show that 4 is not a primitive root modulo any prime p.

Question 2

Give a characterization of primes p for which the congruence math x^4 + 1 \equiv 0 \mod p math has at least one solution.

Question 3

How many solutions does the congruence math 1+x+x^2+\ldots+x^{23} \equiv 0 \mod 111 math have?

Question 4

Show that every prime divisor p>3 of math n^2+n+1 math is congruent to 1 modulo 6.