The Pure Mathematics department teaches number theory courses at various levels. Over the centuries, this discipline has grown very much with close connections to other areas of mathematics: algebraic geometry, representation theory, combinatorics, cryptography and coding theory, probability, harmonic analysis and complex analysis.

The great difficulty in proving relatively simple results in number theory prompts many new concepts in mathematics. Wiles after the cumulative effort of many mathematicians for more than 350 years, while the twin prime conjecture remains open even today. Fermat's last theorem was only proved in 1995 by A. Although these questions are easily stated, they are so deep that they have withstood attempts to prove them for centuries. The twin prime conjecture is to ask if there should be infinitely many primes p such that p+2 is also a prime. For example, the famous last theorem of Fermat states that there exists no non-trivial integer solution of the equation x n + y n = z n for n ≥ 3. Many problems in number theory can be formulated in a relatively simple language. Gauss, who is often known as the 'prince of mathematics', called mathematics the 'queen of the sciences' and considered number theory the 'queen of mathematics'.

The multiplicative Inverse of 2412 isĬlarification: The multiplicative Inverse does not exist as GCD (24140, 40902) = 34.Unsurprisingly, number theorists are interested in the properties of numbers! In particular, the relations between the additive and multiplicative structures of integers are so fascinating that they make number theory a vast and fertile field of mathematical research. Or in this case 15 mod 13 = 2.Ĭlarification: The multiplicative Inverse of 12 is 3239.Ĭlarification: The multiplicative Inverse of 5 is 550.ġ3. The correct equivalence would be mod n = (a – b) mod n.Ĭlarification: The correct answer is 2. mod n = (b – a) mod nĬlarification:The equivalence is false and can be checked by substituting values. mod n = (a+b) mod nĬlarification: The equivalence is true and can be checked by substituting values.ĩ. Which of the following is a valid property for concurrency?Ĭ) a = b (mod n) and b = c (mod n) implies a = c (mod n)Ĭlarification: All are valid properties of congruences and can be checked by using substituting values.Ĩ.

Cryptography Multiple Choice Questions on “Number Theory”.Ĭlarification: The statement is true.

Basic number theory questions