NUMBER THEORY AND CRYPTOGRAPHY QUIZ

If a|b and b=aq+r, then

• r=0

• 0 < r < a

• 0 <= r < a

• 0 <= r <= a

If g=(a,b), d|a,d|b then

• d | g

• g | d

• a| g

• b | g

If (x/g,y/g)=1then (x,y)=

• 1

• (x/g , y/g)

• g

• (g/x , g/y)

For any integer x,y, the least positive of ax+by=

• 1

• (a, b)

• [a, b]

• (a, b) [a, b}

a*b=

• (a,b) [a,b]

• (a,b) /[a,b]

• [a,b]/ (a,b)

• (a,b) +[a,b]

For any odd integer n, n≡1 or −1(mod 2) 

• false

• true

If b ≡ c ( mod m) then (b, m)= 

• (b+c , m)

• (b-c , m)

• (b, m)

• (c, m)

If p is prime  a^(p−1) ≡ ________ (mod p)​ 

• 1

• 0

• -1

• a

{a₁​,a_2​, ...,a_r​} is RRS mod m   and for any integer y,    y ≡ a_i​ (mod m) some i  if ___________

• (y , a_i) = 1 for all i(

• (y , a_i) = 1 for some i

• (y, m) =1

• (y , a_i)=1 and (a_i , a_j) =1

6! Ξ _______ ( mod 7)

• 1

• -1

• 0

• none of these