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In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is not equal to zero. All integers are rational, including zero.
Triangle with the area 6, a congruent number. In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. [1] [2] A more general definition includes all positive rational numbers with this property. [3] The sequence of (integer) congruent numbers starts with
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
Rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. [9] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold).
Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression of positive definite rational functions as sums of quotients of squares .
The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p / q is a "good" approximation of a real number α if the absolute value of the difference between p / q and α may not decrease if p / q is replaced by another rational number with a smaller denominator.
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