Week 1 - Mathematics and Computer Studies
... When such a cryptosystem is used, the public key is known to everybody. It can be used to encrypt messages. However, only the holder of the private key is able to decrypt such a ciphertext. Nowadays, internet data security is based on such cryptographic techniques. Public key cryptography is not onl ...
... When such a cryptosystem is used, the public key is known to everybody. It can be used to encrypt messages. However, only the holder of the private key is able to decrypt such a ciphertext. Nowadays, internet data security is based on such cryptographic techniques. Public key cryptography is not onl ...
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... Suppose dja and djb. Then dj(a b) Thus every common divisor of a and b is a common divisor of b,a b. Suppose djb and dja b, then djb + (a b) that is dja. Thus every common divisor of b and b a is a common divisor of a and b. In other words all common divisors are same, or more speci cally the Greate ...
... Suppose dja and djb. Then dj(a b) Thus every common divisor of a and b is a common divisor of b,a b. Suppose djb and dja b, then djb + (a b) that is dja. Thus every common divisor of b and b a is a common divisor of a and b. In other words all common divisors are same, or more speci cally the Greate ...
Finding Real Roots of Polynomial Equations
... Who uses this? Package designers can use roots of polynomial equations to set production specifications. Previously, you have learned several methods for factoring polynomials. As with some quadratic equations, factoring a polynomial equation is one way to find its real roots. Recall the Zero Produc ...
... Who uses this? Package designers can use roots of polynomial equations to set production specifications. Previously, you have learned several methods for factoring polynomials. As with some quadratic equations, factoring a polynomial equation is one way to find its real roots. Recall the Zero Produc ...
Practice 2-4
... 1. Classify the equation 7x + 3 = 7x – 4 as having one solution, no solution, or infinitely many solutions. 2. Classify the equation 4x + 2 = 4x + 2 as having one solution, no solution, or infinitely many solutions. 3. Which answer shows the correct solution for 6x + 19x – 4 = 5(5x + 4)? If neces ...
... 1. Classify the equation 7x + 3 = 7x – 4 as having one solution, no solution, or infinitely many solutions. 2. Classify the equation 4x + 2 = 4x + 2 as having one solution, no solution, or infinitely many solutions. 3. Which answer shows the correct solution for 6x + 19x – 4 = 5(5x + 4)? If neces ...
Irrationality of the Zeta Constants
... a general technique for proving the irrationality of the zeta constants ζ(2n + 1) from the known irrationality of the beta constants L(2n + 1, χ), 1 6= n ∈ N. This technique provides another proof of the first odd case ζ(3), which have well known proofs of irrationalities, see [1], [2], [16], et al, ...
... a general technique for proving the irrationality of the zeta constants ζ(2n + 1) from the known irrationality of the beta constants L(2n + 1, χ), 1 6= n ∈ N. This technique provides another proof of the first odd case ζ(3), which have well known proofs of irrationalities, see [1], [2], [16], et al, ...
Full text
... In one of his famous results, Fermat showed that there exists no Pythagorean triangle with integer sides whose area is an integer square. His elegant method of proof is one of the first known examples in the history of the theory of numbers where the method of infinite descent is employed. Mohanty [ ...
... In one of his famous results, Fermat showed that there exists no Pythagorean triangle with integer sides whose area is an integer square. His elegant method of proof is one of the first known examples in the history of the theory of numbers where the method of infinite descent is employed. Mohanty [ ...
PDF - UNT Digital Library
... sufficient conditions, which intrinsically characterize measures which belong to the same class. Topologically equivalent measures in the n-dimensional unit cube, the space of irrational numbers in the unit interval, and the Hilbert cube have been studied, respectively, by Oxtoby and Ulam [1], Oxtob ...
... sufficient conditions, which intrinsically characterize measures which belong to the same class. Topologically equivalent measures in the n-dimensional unit cube, the space of irrational numbers in the unit interval, and the Hilbert cube have been studied, respectively, by Oxtoby and Ulam [1], Oxtob ...
Hilbert`s Tenth Problem
... In 1900, David Hilbert gave an address at the International Congress of Mathematicians in which he gave a list of 23 problems that would influence the world of mathematics. In this project, we will focus on his tenth problem. In his tenth problem, Hilbert talks about Diophantine equations, and if th ...
... In 1900, David Hilbert gave an address at the International Congress of Mathematicians in which he gave a list of 23 problems that would influence the world of mathematics. In this project, we will focus on his tenth problem. In his tenth problem, Hilbert talks about Diophantine equations, and if th ...
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. The cases n = 1 and n = 2 were known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The theretofore unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for ""most difficult mathematical problems"".