Let g be primitive modulo 11. How many distinct nonzero remainders occur among g^0, g^2, g^4, g^6 and g^8?

Which set contains all remainders x with x^2 congruent to 4 modulo 7?

• {2, 4}
• {3, 4}
• {2, 5}
• {1, 6}

Modulo 5, which pair lists all nonzero squares?

• {1, 2}
• {1, 4}
• {2, 3}

Modulo 7, the number 2 is a square because 3 squared leaves remainder 2. True or false?

Use the residue-count formula to find the number of nonzero squares modulo 19.

For p = 2, the exponent (p - 1)/2 is an integer, so the stated odd-prime form of Euler's criterion applies. Is this true?

Use Euler's criterion to decide whether 7 is a square modulo 11.

• 7 is a nonsquare modulo 11
• 7 is a nonzero square modulo 11
• 7 is divisible by the prime 11
• 7 has no remainder modulo 11

Modulo 7, 2 raised to the power 3 leaves remainder 1. What does Euler's criterion say about 2?

• 2 is a quadratic nonresidue
• 2 is a quadratic residue
• The criterion gives no answer here

Without computing powers, why is 2 a square modulo 23?

• 23 leaves 7 modulo 8, so (2/23) = 1
• 23 leaves 3 modulo 4, so (2/23) = -1
• 23 is odd and prime, so (2/23) = 0

Use quadratic reciprocity to evaluate (3/29). Enter the Legendre symbol's value.