Advanced Number Theory Test – 8 Hard Questions
A focused set of eight demanding items designed to evaluate expert knowledge of number‑theoretic concepts and techniques.
Quiz Questions
Answer all questions below and test your knowledge.
- 1
Which of the following numbers is NOT a prime factor of 2^{10}‑1?
- 2
Find a solution to the congruence x^{2} ≡ 1 (mod 101).
- 3
What is Euler's totient φ(210)?
- 4
What is the smallest integer n such that n! ends with exactly three trailing zeros?
- 5
Give an integer solution (x,y) to 3x+7y=1 with the smallest positive x.
- 6
Which number is a quadratic residue modulo 13?
- 7
Find the smallest positive integer N satisfying N ≡ 2 (mod 3) and N ≡ 3 (mod 5).
- 8
Which of the following numbers is an even perfect number?
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