Number Theory quiz

More questions about Number Theory

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   What is a whole number greater than 1 that is not prime called?

   Answer: Composite number

   Why: Every composite number can be uniquely broken down into a product of prime factors.

2. 2 Medium

   What taxicab number is the smallest sum of two cubes two ways?

   Answer: 1729

   Why: Bernard Frénicle de Bessy published the same pair of cube sums in 1657, more than 250 years before Ramanujan's taxi ride.

3. 3 Hard

   Legendre's Conjecture states there is always a prime between consecutive what?

   Answer: Perfect squares

   Why: Edmund Landau listed it in 1912 among four prime problems he called unattackable, and all four are still open today.

4. 4 Easy

   In which number sequence is each term the sum of the previous two?

   Answer: Fibonacci sequence

   Why: Introduced to Western Europe in 1202 by Fibonacci to track ideal rabbit population growth, its ratios converge to the Golden Ratio.

5. 5 Medium

   Modern internet encryption relies on the difficulty of factoring products of what?

   Answer: Large prime numbers

   Why: In 2020 it took roughly 2,700 core years of computing to split a 250 digit RSA number back into its two 125 digit factors.

6. 6 Hard

   Which insects use prime-numbered lifecycles of 13 or 17 years to avoid predators?

   Answer: Cicadas

   Why: Two broods surfaced together in 2024 for the first time since 1803, and the next joint emergence is due in 2245.