Hard Number Theory Quiz: Seven Expert-Level Problems

A set of seven challenging questions designed for seasoned mathematicians interested in integer properties and proofs.

prime numbersPell equationFermatEuler theoremquadratic residuesDiophantinemodular arithmetic

Difficulty:HARD

Questions7

CategoryMathematics & Logic

DifficultyHARD

Progress

0/0

Quiz Questions

Answer all questions below and test your knowledge.

1
Identify the smallest integer greater than one thousand that is not divisible by any smaller integer greater than one and leaves remainder one upon division by four.
Question 1
2
Which integer between 2 and 12 satisfies the congruence x² ≡ 1 (mod 13)?
Question 2
3
What is the sum of all positive divisors of 28?
Question 3
4
Find the smallest non‑trivial solution (x,y) to the equation x²‑2y² = 1.
Question 4
5
Determine the least positive integer n such that n ≡ 2 (mod 5) and n ≡ 3 (mod 7).
Question 5
6
Compute Euler's totient function φ(100).
Question 6
7
Which integer less than 200 has no divisor other than one and itself and can be expressed as the sum of two squares, and is the greatest with this property?
Question 7