C9-12

Question 1

what formula is used for the check digit x10 (sub)

Answer 1

1x1 +2x2… +9x9 + 10x10 ≡ 0 (mod 11)
(where it is x, not multiplications and the latter numbers are subs)
or equivalently:
x10 ≡ 1x1 + 2x2… 8x8 + 9x9 (modd 11)

Question 2

what formula is used for the check digit x13 (sub) E {0, 1, 2..9}

Answer 2

x1 + 3x2 + x3 + 3x4 + .. 3x12 + x13 ≡ 0 (mod 10)

Question 3

What are the four blocks an EAN-13 bar code consists of?

Answer 3

the number system, the manufacturer code, the product code and the check digit.

Question 4

what digits represent the bank number if the card number begins with 51

Answer 4

the second and third

Question 5

what digits represent the bank number if the card number begins with 52

Answer 5

second, third and fourth

Question 6

what digits represent the bank number if the card number begins with 53

Answer 6

second, third, fourth and fifth

Question 7

what digits represent the bank number if the card number begins with 54 or 55

Answer 7

digits from second place to the sixth place

Question 8

what do the digits after the bank number up to the 15th digit represent?

Answer 8

they form the account number of the card

Question 9

what does the 16th digit of the bank number represent

Answer 9

it is the check digit

Question 10

what is the formula for affine ciphers

Answer 10

y ≡ mx + s (mod n)

where using numerical-alphabet n=26

Question 11

If x ≡ r (mod m)

Answer 11

then we call r a residue of x modulo m.

Question 12

When is a set of integers {r1…rs} called a complete residue system modulo m

Answer 12

if for each integer n there is an i, 1 less than or equal to i which is less than or equal to s such that n ≡ ri (mod m)

Question 13

When is a set of integers {r1…rs} called a reduced residue system modulo m

Answer 13

if gcd (ri, m) = 1 for each 1 less than or equal to i less than or equal to s

for each integer n relatively prime to m there is an i, 1 less than or equal to i which is less than or equal to s such that n ≡ ri (mod m)

Question 14

for each positive integer m, what is ϕ(m)

Answer 14

ϕ(m) is the number of positive integers between 1 and m inclusive which are relatively prime to m

Question 15

when is ϕ(m) = m true?

Answer 15

when m is 1 and this is the only solution

Question 16

when is ϕ(p) = p-1

Answer 16

for any prime p: all positive integers less than p are relatively prime to p

Question 17

if p and q are two distinct primes, what is ϕ(pq)

Answer 17

=ϕ(p) ϕ(q) = (p-1) (q-1)

Question 18

m is a positive integer such that gcd(a,m)=1

a^(ϕ(m)) ≡ ?

Answer 18

≡ 1 (mod m)

Question 19

for any prime p and any integer a such that a does not divide into p:
a^(p-1) ≡ ?

Answer 19

≡ 1 (mod p)