NUMBER THEORY AND CRYPTOGRAPHY QUIZ - UNIT 1 & 2

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)=1 then (x,y)=

• 1

• (x/g , y/g)

• g

• (g/x , g/y)

For any integers x,y, the least positive of the form 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]

The Factoring of any integer n>1 into primes is unique apart from the order of prime factors.

• Fundamental theorem of Number theory

• Fundamental theorem of Arithmetic

If (a, b) = 11, [a, b] = 693 and a = 77 then b =?

• 11

• 99

• 66

• 33

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