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Question 1
a) Compute
b) Compute
Question 2
If
is prime, show that 3 is not a quadratic residue.
Combine this with the result of question 2 from
March 1
to conclude that every number not divisible by p is congruent to a power of 3 modulo p.
Question 3
For what primes p the number 5 is a quadratic residue?
Question 4
Show that any prime number p which is congruent to 1 modulo 6 is a divisor of some number of the form
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a) Compute
b) Compute
Question 2
If
is prime, show that 3 is not a quadratic residue.
Combine this with the result of question 2 from March 1 to conclude that every number not divisible by p is congruent to a power of 3 modulo p.
Question 3
For what primes p the number 5 is a quadratic residue?
Question 4
Show that any prime number p which is congruent to 1 modulo 6 is a divisor of some number of the form