Addition fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Cubic fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Division fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Division I
Compute $val10/$val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 0 and $val8.
Division II
Compute $val10/$val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 0 and $val8.
Division III
Compute $val10/$val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 0 and $val8.
Zero divisors
Is $val7 a zero divisor in $m_ZZ/$val6$m_ZZ ?
Zero divisor II
Find the set of zero divisors in $m_ZZ/$val6$m_ZZ. (In this exercise we don't consider 0 as a zero divisor.) Write each element by a number between 1 and $val7, and separate the elements by commas.
Zero divisors III
We have $val7=$val62, where $val6 is a prime. How many zero divisors there are in $m_ZZ/$val7$m_ZZ ? In this exercise we don't consider 0 as a zero divisor.
Inverse I
Find the inverse of $val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 0 and $val8.
Inverse II
Find the inverse of $val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 1 and $val8.
Inverse III
Find the inverse of $val9 in $m_ZZ/$val7$m_ZZ. The result must be represented by a number between 0 and $val8.
Invertible power
$val9 is a prime. Consider the function f: $m_ZZ/$val9$m_ZZ -> $m_ZZ/$val9$m_ZZ defined by f(x)=x$val14 . Is f bijective?
Multiplication fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Polynomial fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Powers
Compute the element $val9$val7 in $m_ZZ/$val6$m_ZZ. The result must be represented by a number between 0 and $val8.
Powers II
$val6 is a prime number. Compute the element $val9$val7 in $m_ZZ/$val6$m_ZZ. The result must be represented by a number between 0 and $val8.
Power fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.
Roots
$val6 is a prime number. There is an element a in $m_ZZ/$val6$m_ZZ, such that a$val10 is congruent to $val16 modulo $val6. Find a. The result must be represented by a number between 0 and $val7.
Simple computations modulo n
Compute $val13 in $m_ZZ/$val6$m_ZZ. The result must be represented by a number between 0 and $val7.
Squares
Find the set of squares in $m_ZZ/$val6$m_ZZ. (A square in $m_ZZ/$val6$m_ZZ is an element which is the square of another one.) Write each element by a number between 0 and $val7, and separate the elements by commas.
Sum and product
Find two integers $val7, $val8 such that 0
$val7
$val10 , 0
$val8
$val10 , $val7 + $val8
$val13 (mod $val9) , $val7 × $val8
$val14 (mod $val9) .
You may enter the two numbers in any order.
Trinomial fill
Consider a map
, which sends
to
. Fill the following table for
by dragging the numbers given below.