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Mathematical Theorems
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Can you name the mathematical theorems?
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Noether
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Theorems range from high-school algebra to college-level math and beyond.
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Description
Theorem
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere
For all real numbers x and y, |x+y| is less than or equal to |x| + |y|
Every natural number greater than 1 either is prime or can be expressed uniquely (up to order) as a product of primes.
If G is a finite group and H is a subgroup of G, then the order of H divides the order of G
A polynomial f(x) has a factor (x-k) if and only if f(k) = 0
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a^2+b^2=c^2
Every non-self-intersecting closed curve in the plane divides the plane into a distinct inside and outside
If p is prime, then a^p is congruent to a (mod p)
Description
Theorem
There is no general solution in radicals to polynomial equations of degree 5 or higher
If n is a natural number greater than 1, there exists a prime p such that n < p < 2n
The equation x^n+y^n=z^n has no nontrivial integer solutions when n > 2
There exist arbitrarily long arithmetic sequences of primes
The number of primes less than n is asymptotic to n/(ln n)
Every sufficiently large even integer can be written either as the sum of two primes, or as the sum of a prime and a semiprime
If a real-valued function f is continuous on [a,b] and differentiable on (a,b) and f(a) = f(b), there exists c in (a,b) such that f'(c) = 0
If a real-valued function f is continuous on the interval [a,b], then f assumes a maximum and minimum value on that interval
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