NEW
Font size
WorksheetsNUMBER THEORY AND CRYPTOGRAPHY QUIZ - UNIT 1 & 2
Total questions: 20
Worksheet time: 15mins
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
If (a, m)=1 and ax ≡ b (mod m) then x=
aϕ(m)
aϕ(m)-1
aϕ(m)b
aϕ(m)-1 b
6! Ξ _______ ( mod 7)
1
-1
0
none of these
If {a1,a2, ...,ar} is a CRS mod m then for any integer y, y ≡ ai and aj(mod m) i ≠ j
true
false
ϕ(m,n) = ϕ(m) ϕ(n) for any integer n,m
true
false
A set {a1,a2, ... ,ar} is a RRS mod m and for any integer y, y ≡ ai (mod m) some i if ___________
(ai , aj) = 1
(y, m) = 1
(y, ai )=1 and (y, m) =1
( ai , m) =1 and (y, m) = 1
There are no large gaps in the series of primes
True
False
If a = 2*5*7*2*3 and b = 3*3*5 then (a,b) =
2*3*5*7
3*3*5
2*2*3*3*5*7
3*5
If a = 2*5*7*2*3 and b = 3*3*5 then [a,b] =
2*3*5*7
3*3*5
2*2*3*3*5*7
3*5
(ma, mb) =
(mb, ma)
m(a,b)
both are true
none of these
If p is prime, p| ab then
p|a and p|b
p|a or p|b
p|a (only)
p|b (only)
