Based on Facts
Divide and Conquer
Modular Mayhem
Mass Market Appeal
Practical Problems
100

The prime factorization of 5280.

What is 25*3*5*11?

100

A statement that is true if a|b and b|c.

What is a|c?

100

The solution of 2 mod 17.

What is 2?

100

The largest integer that divides two other integers.

What is the Greatest Common Denominator (GCD)?

100

The time a 24-hour clock will read 100 hours after it reads 2:00?

What is 6:00?

200

The decimal number 32 expressed in base 6.

What is 526?

200
A binary operator which takes two integers and returns a boolean (true or false) value.

What is divides?

200

An expression that a≡b(modm) is equivalent to by the definition of modular congruence.

What is m|(a-b) or mk = a-b, where k ∈ ℤ?

200

The GCD of 754 and 78.

What is 26?

200

The smallest possible integer, n, such that 540n = n4.

What is 1500?

300

What is the largest prime factor of 50!

What is 47?

300
An equivalent expression to a|b by the definition of divides.

What is a*k = b, where k ∈ ℤ?

300

The smallest positive modular inverse of 3 mod 7.

What is 5?

300

The LCM of 32 and 38.

What is 608?

300

All the primes greater than 100 but less than 150 (inclusive).

What are 101, 103, 107, 109, 113, 127, 131, 137, 139, and 149?

400

The smallest base in which 235 and 94 both end with a zero. 

What is base 47?

400

A proof that if a|b and a|c, then a|bc.

What is something I will go over shortly?
400

A solution to the linear congruence 4x=5(mod 9).

What is 8?

400
The amount of times it would take Stanley to measure 1 gallon with a 69 and a 250 gallon container.

What is 61?

500

The total quantity of factors 360 has.

What is 24?

500

A proof that a, b ∈ ℤ, if 17|2a + 3b, show that 17|9a + 5b.

What is:
17k=2a+3b

500

A solution to the linear congruence x ≡ 2 (mod 3), x ≡ 1 (mod 4), x ≡ 3 (mod 5).

What is 233?

500

The smallest quantity of bagels Jamés must purchase such that a. If James has 9 friends, he has 3 bagels left over. b. If James has 10 friends, he has 2 bagels left over. c. If James has 11 friends, he has 4 bagels left over.

What is 642 bagels?