AOPS NUMBER THEORY

Find all the perfect cubes between 1000 and 2000

• 1331,1728

• 1231, 1887

• 1000,2197

• 1121, 1997

Find the smallest positive integer that is not a divisor of 5040

• 17

• 11

• 13

• 16

What is the largest two-digit prime number whose digits are also each prime?

• 53

• 67

• 73

• What is a prime?

• 5

• 3

• 2

• 7

gcd(129, 311)

• 21

• 22

• 07

• 01

How many of the first 100 positive integers are divisible by 7?

• 15

• 11

• 12

• 14

The GCD of n and 216 is 24 and their LCM is 864. Find n.

• 96

• 72

• 24

• 144

How many positive integers are divisors of 999,999?

• 27

• 53

• 64

• 90

• 6

• 3

• 5

• 4

Find the number of five-digit palindromes.

• 455

• 675

• 760

• 900