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Q1
Solve the congruence
Q2
For what value of a does the congruence
have exactly one solution?
Q3
Show that if
is prime, then
Hint: order of an element modulo a prime p divides p1
Q4
How many elements of order 6 are there modulo 13? List them all.
How many elements of order 5 are there modulo 13?
Q5
How many polynomials
of degree k with coefficients 0 and 1 don't have any roots modulo 2?
How many have exactly two roots?
Can such a polynomial have more than two roots?
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Solve the congruence
Q2
For what value of a does the congruence
have exactly one solution?
Q3
Show that if
is prime, then
Hint: order of an element modulo a prime p divides p1
Q4
How many elements of order 6 are there modulo 13? List them all.
How many elements of order 5 are there modulo 13?
Q5
How many polynomials
of degree k with coefficients 0 and 1 don't have any roots modulo 2?
How many have exactly two roots?
Can such a polynomial have more than two roots?