Questions & Answers
Browse all 25 questions from the
History of Number Theory study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
Which ancient clay tablet, dating to the Old Babylonian period, contains a list of Pythagorean triples?
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A
Plimpton 322
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B
Rhind Papyrus
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C
Moscow Papyrus
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D
Berlin Papyrus
2
Who is credited with providing the first rigorous proof of the Infinitude of Primes in his work 'Elements'?
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A
Archimedes
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B
Euclid
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C
Pythagoras
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D
Diophantus
3
Pierre de Fermat famously claimed to have a proof for which theorem in the margin of his copy of Diophantus's 'Arithmetica'?
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A
Fermat's Little Theorem
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B
Fermat's Polygonal Number Theorem
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C
Fermat's Last Theorem
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D
Fermat's Two-Square Theorem
4
Which mathematician finally proved Fermat's Last Theorem in 1994?
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A
Andrew Wiles
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B
Leonhard Euler
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C
Carl Friedrich Gauss
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D
Kurt Gödel
5
The study of modular arithmetic was formalized in the 1801 book 'Disquisitiones Arithmeticae' by which mathematician?
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A
Bernhard Riemann
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B
Joseph-Louis Lagrange
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C
Carl Friedrich Gauss
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D
Augustin-Louis Cauchy
6
Which 18th-century mathematician discovered the formula relating the sum of the reciprocals of primes to the natural logarithm?
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A
Leonhard Euler
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B
Isaac Newton
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C
Gottfried Leibniz
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D
Brook Taylor
7
The Goldbach Conjecture, proposed in 1742, suggests that every even integer greater than 2 is the sum of two what?
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A
Perfect numbers
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B
Prime numbers
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C
Triangular numbers
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D
Square numbers
8
What is the name of the function, denoted by phi(n), that counts the positive integers up to n that are relatively prime to n?
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A
Euler's totient function
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B
Riemann zeta function
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C
Mobius function
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D
Dirichlet function
9
Which mathematician developed the 'Sieve of Eratosthenes', an ancient algorithm for finding all prime numbers up to any given limit?
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A
Eratosthenes of Cyrene
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B
Hypatia of Alexandria
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C
Pappus of Alexandria
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D
Apollonius of Perga
10
The 'Arithmetica', a major work on number theory that influenced Fermat and others, was written by whom?
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A
Diophantus
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B
Plato
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C
Thales
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D
Hipparchus
11
In 1859, Bernhard Riemann published a paper that introduced which famous function, central to the study of prime number distribution?
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A
Riemann zeta function
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B
Gamma function
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C
Beta function
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D
Elliptic function
12
The 'Prime Number Theorem', describing the asymptotic distribution of prime numbers, was independently proved in 1896 by which two mathematicians?
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A
Hadamard and de la Vallée Poussin
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B
Hardy and Littlewood
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C
Hilbert and Cantor
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D
Cauchy and Abel
13
Which English mathematician is known for his extensive work on the distribution of primes and his collaboration with Ramanujan?
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A
G.H. Hardy
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B
Alan Turing
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C
Charles Babbage
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D
Bertrand Russell
14
Srinivasa Ramanujan, a self-taught mathematical genius, made significant contributions to number theory from which country?
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A
India
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B
Japan
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C
Brazil
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D
South Africa
15
The 'Law of Quadratic Reciprocity' was first conjectured by Euler and Legendre, but the first published proof was provided by whom?
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A
Carl Friedrich Gauss
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B
Pierre de Fermat
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C
Blaise Pascal
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D
Joseph Fourier
16
Which 17th-century French mathematician and monk conducted extensive correspondence on number theory and is the namesake of the Mersenne primes?
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A
Marin Mersenne
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B
René Descartes
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C
Blaise Pascal
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D
Pierre Gassendi
17
Sophie Germain made a major breakthrough toward proving Fermat's Last Theorem by proving the result for a specific class of primes now known as:
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A
Sophie Germain primes
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B
Gaussian primes
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C
Mersenne primes
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D
Fermat primes
18
What is the name of the constant, denoted by gamma, that appears in the context of the harmonic series and Euler-Mascheroni?
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A
Euler-Mascheroni constant
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B
Feigenbaum constant
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C
Khinchin constant
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D
Landau constant
19
The 'ABC conjecture', a major unsolved problem in number theory, deals with the relationship between the radical of the product of three coprime integers, and was proposed in:
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A
1985
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B
1750
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C
1920
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D
2005
20
Which mathematician introduced the concept of 'Gaussian integers' (numbers of the form a + bi where a and b are integers)?
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A
Carl Friedrich Gauss
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B
Augustin-Louis Cauchy
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C
Niels Henrik Abel
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D
Évariste Galois
21
The 'Four-Square Theorem', stating that every natural number can be represented as the sum of four integer squares, was proved by:
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A
Joseph-Louis Lagrange
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B
Pierre de Fermat
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C
John Wallis
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D
Isaac Barrow
22
What is the name of the 19th-century mathematician who contributed significantly to number theory through his work on the 'Dirichlet series'?
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A
Peter Gustav Lejeune Dirichlet
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B
Carl Jacobi
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C
Karl Weierstrass
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D
Bernhard Riemann
23
A 'Perfect number' is a positive integer that is equal to the sum of its proper divisors. Which is the smallest perfect number?
24
Which mathematician formulated the 'Prime Number Theorem' as a conjecture based on analyzing tables of primes?
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A
Adrien-Marie Legendre
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B
Carl Friedrich Gauss
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C
Leonhard Euler
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D
Joseph-Louis Lagrange
25
The 'Wolfskehl Prize' was established in 1908 to reward the proof of which famous mathematical problem?
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A
Fermat's Last Theorem
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B
Goldbach Conjecture
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C
Twin Prime Conjecture
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D
Riemann Hypothesis
