Cryptology
The algorithm that is used to encrypt information over the internet.
What is the RSA Algorithm?
What does it mean to say c = a (mod b)?
c and a both have the same remainder when divided by b.
This is the contradictory statement to: "If A then B".
What is "If A then not B".
This is defined as the probability that one event occurs has no affect of the probability of another event occurring.
What is an independent event?
This is the number of times you can subtract 5 from 25.
What is once?
This is the modulus for any Caesar Cipher encryption.
What is 26?
This is the solution to 100 (mod 12).
What is 4?
This is the contrapositive statement to: If A then B.
If not B, then not A
If the probability of getting an A is (7/10) and the probability of catching the bus after class is (4/5), this the probability that both events will happen at the same time.
What is (7/10)*(4/5) = 28/50?
What two whole, positive numbers that have a one-digit answer when multiplied and a two-digit answer when added?
This theorem is the basis for the RSA Algorithm.
What is Fermat's Little Theorem.
This is the modulus when you want to find an x that is congruent to the following equations:
x = 4 (mod 7)
x = 5 (mod 3)
What is 21?
The definition of a rational number is that a rational number's decimal places can be represented by p/q where p and q must be this mathematical term. (Hint: it was what we used to prove the square root of 2 was irrational).
What is coprime or relatively prime?
This is the number of ways someone could arrange 5 backpacks in a row, each with a different color.
What is 5*4*3*2*1?
Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
The phrase "I LOVE NUMBERS" can be encoded when 23(mod 26) is added to each letter to this code.
What is "F ILSB KRJYBOP"?
This is one solution for x to 3x = 4 (mod 5)
What is x = 3?
Prove by direct proof: 2b^3 + 1 is odd
b = 2k +1
2*(2k+1)^3 + 1We know (2k+1)^3 will be an integer.
2*integer + 1 = odd number.
This is the number of ways to arrange 10 books into 4 different spots on a shelf.
If
12 + 12 = 9
25 + 25 = 49
18 + 18 = 81
What is 29 + 29 = ?
What is (2+9)^2 = 121?
This modulus and remainder of the Caesar Cipher will shift "MATH" to "DOHV".
What is letter # + 17(mod 26).
This is the general solution to x for the following equation: x + 30 (mod 12) = 1 (mod 12).
What is 19 + 12k where k is an integer?
Prove by contradiction: If a and b are integers, the product is odd if and only if a and b are both odd.
Contradictory Statement: If a and b are integers, the product is odd if and only if a and b are both even.
a = 2k1
b = 2k2
a*b = (2k1)*(2k2) = 4(k1*k2) = even
If there is a group of 4 girls and 6 boys a 3 members are randomly selected from the group to join a committee, this is the probability of picking 2 girls and one boy from this group.
What is [(4 choose 2)*(6 choose 1)]/(10 choose 3)
If 2 = 5
3 = 10
4 = 17
What does 5 = ?5 = 26