Maths Olympiad Prep

Library / /31 of 520

Number theory Difficulty 5.3 AIME, harder Find the answer

8. Which positive integers have exactly
a) two positive divisors
b) three positive divisors
c) four positive divisors?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solutions — 2

Solution 1

8. a) primes
b) squares of primes primes
c) products to two distinct primes or cubes of

Solution 2

8. a) primes
b) squares of prime primes
c) products of two distinct primes or cubes of

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.