- #1
Suvadip
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Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
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How to proceed?
suvadip said:Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
How to proceed?
suvadip said:Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
How to proceed?
suvadip said:Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
How to proceed?
Number theory is a branch of mathematics that studies the properties and relationships of integers and other numbers. It is a fundamental area of mathematics that has applications in various fields such as cryptography, computer science, and physics.
Prime numbers are positive integers that are divisible only by 1 and themselves. They play a crucial role in number theory as they are the building blocks of all other integers. The first few prime numbers are 2, 3, 5, 7, 11, and so on.
The Goldbach conjecture is an unsolved problem in number theory, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers. This conjecture has been tested for millions of even numbers, but it has not been proven or disproven yet.
The Riemann hypothesis is one of the most famous unsolved problems in mathematics. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line with real part 1/2. This hypothesis has far-reaching implications in number theory, but it remains unproven.
Number theory plays a crucial role in modern cryptography by providing the mathematical foundation for secure communication. Prime numbers, modular arithmetic, and other concepts from number theory are used to create secure encryption algorithms and digital signatures.