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Mathematical Theorems
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Can you name the mathematical theorems?
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Click the green button to start and enter the correct answers below
Theorems range from highschool algebra to collegelevel math and beyond.
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Description
Theorem
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
If n is a natural number greater than 1, there exists a prime p such that n < p < 2n
A polynomial f(x) has a factor (xk) if and only if f(k) = 0
Every natural number greater than 1 either is prime or can be expressed uniquely (up to order) as a product of primes.
If a realvalued 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
For all real numbers x and y, x+y is less than or equal to x + y
There is no general solution in radicals to polynomial equations of degree 5 or higher
The number of primes less than n is asymptotic to n/(ln n)
Description
Theorem
If p is prime, then a^p is congruent to a (mod p)
Every nonselfintersecting closed curve in the plane divides the plane into a distinct inside and outside
If a realvalued function f is continuous on the interval [a,b], then f assumes a maximum and minimum value on that interval
If G is a finite group and H is a subgroup of G, then the order of H divides the order of G
The equation x^n+y^n=z^n has no nontrivial integer solutions when n > 2
There exist arbitrarily long arithmetic sequences of primes
Every simply connected, closed 3manifold is homeomorphic to the 3sphere
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
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