Number Theory Quiz

Explain Bezout's Theorem , for a,b coprime integers

• Bezout's Theorem is used to calculate the area of a triangle

• p|ab => p|a, p|b

• xa +yb = 1

• xa + yb = c

Implement Euclid's Algorithm to find the GCD of 48 and 18.

• The GCD of 48 and 18 is 24.

• The GCD of 48 and 18 is 6.

• The GCD of 48 and 18 is 36.

• The GCD of 48 and 18 is 12.

Solve the following number theory problem: If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?

• 4

• 2

• 6

• 1

Tags

CCSS.7.NS.A.2A

CCSS.7.NS.A.2B

Calculate the GCD of 84 and 18 using Euclid's Algorithm.

• 6

• 10

• 12

• 20

State Fermat's Little Theorem and explain its significance in number theory.

• Fermat's Little Theorem states that a^(p-1) is congruent to 0 modulo p.

• Fermat's Little Theorem guarantees that a is divisible by p.

• Fermat's Little Theorem states that if p is prime and a is any integer coprime to p, then a^(p-1) is congruent to 1 modulo p.

• Fermat's Little Theorem applies only to even prime numbers.

Using Bezout's Theorem, find integers x and y such that 35x + 15y = 5.

• x = -1, y = 2

• x = 0, y = 1

• x = 1, y = -2

• x = 3, y = 4

Find the GCD of 105 and 42 using Euclid's Algorithm.

• 21

• 28

• 15

• 35

using Fermat's Little Theorem which statement is true (If p is a prime number,)

• 17^17≡ 17(mod 17)

• 23^16≡ 1 (mod 17)

• p^2 ≡ 2 (mod 24)

• p^2 ≡ 1 (mod 24)

does the following eqn has a solution 56x + 72y = 9

• yes

• no

Determine the GCD of 63 and 27 using Euclid's Algorithm.

• 18

• 15

• 9

• 12