For every group G, the identity of G is

Any binary operation define on a singleton set is

X o Y = ?

For every group G the number of elements in G is called the

The group in has _______________ element

________________ f(x) $\epsilon$ F(x) and a  $\epsilon$  F, remainder in the division of f(x)

Is z2 [x]/ (s(x)) an integral domain

give the characteristic for z₁₁

give the characteristic for Q[x]

Find the orders n for all fields GF(n), where 100<n<150

give the characterstic for z_{11 [x]}

Euclid algorithm is used or finding

Who invented Euclid algorithm

If 4 is the GCD of 16 and 121 what is the GCD of 12 and 14

Euclidean algorithm does not require the calculations of prime factors

The (a,b) if b = 1 ?

Find (a,b) if b = a²

A linear diophantine equation ------- variables

compute  $\sigma$  (u) for 36

Find the remainder when 16 ,53 is divided by 7

compute the remainder when 3²⁴⁷ is divided 25 desired remaind

Solve the congruence  x $2$   $\equiv$  1(mod) for each modulo m6

True or False
i) If the Congruence x2  $\equiv$  1 (mod m) exactly two solutions

Find the remainder when 30²⁰²⁰ is divided by 19

 $\equiv$ 

solve the linear congruence of 25 x    $\equiv$  30(mod 18)

 $\phi$  

Find   $\phi$  (18)

find   $\phi$  (11)

 $\sigma$  

Compute      $\sigma$  (36)

 $\tau$  

Compute         $\tau$   (18)

 $\phi=H\subset G$  

Let G be a group and       $\phi=H\subset G$  .If H is agroup  under binary operation of g ,then H a subgroup of G

If G is a finite group of order n with H is a sub group of order m,then m divides n

determine all of the polynomials of degree 2 in Z₂ [x]

If R is a ring then (R[x] ,+ .* ) s a

If m pigeons are assigned to n pigeons holes , where m>n, then atleast two pigeon must occupie the same pigeon hole

Express 10110_two in base ten

Express 3014 in base eight

Find the value of the base b

1001_b = 9

fnd (a,b) if b = a²

The simplest class of diop hantine equations is the class of

  Find the remainder when 24^1947 is divided by 17 

Find      $\phi$  28

 $\phi$  

Compute         $\phi$   (p!) for the prime 7

 $\tau$  

Let n be a positive integer then          $\tau$  (n) denotes the number o positive factors of n

 $\phi\ \left(m\right)\ \equiv\ 1$  

Let m be a positive integer and a any integer with (a,m) =1 then a^             $\phi\ \left(m\right)\ =\ 1$   (mod m)