Number Theory Quiz II(2024-2025)

Who introduced the concept of congruence in number theory?

• Leonhard Euler

• Isaac Newton

• Carl Friedrich Gauss

• Bernhard Frenicle de Bessy

What is the sum of all integers from 1 to 100 as discovered by Gauss?

• 100

• 10100

• 2500

• 5050

What does the notation a ≡ b (mod n) signify?

• a and b are equal

• n divides the difference a - b

• a is greater than b

• a is less than b

Which theorem states that if a ≡ b (mod n), then ca ≡ cb (mod n)?

• Theorem of Addition

• Theorem of Equality

• Fermat's Little Theorem

• Theorem of Congruences

Say True or False: 3 = 24 (mod 7)

• True

• False

The smallest pseudoprime number is ---------------

What is the significance of the number 561 in number theory?

• It is an absolute pseudoprime

• It is a prime number

• It is a perfect square

• It is a rational number

What does Wilson's theorem state?

• If p is prime, then (p - 1)! ≡ -1 (mod p)

• If p is prime, then p divides (p - 1)! + 1

• If p is prime, then p divides p!

• If p is prime, then p is odd

Which of the following is a pseudoprime to the base 2?

• 1105

• All of the above

• 561

• 341

If n is an odd pseudoprime, then Mn = 2ⁿ - 1 is a larger one.

• False

• True