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# Famous conjectures

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### Famous conjectures

1. 1. Famous conjectures<br />TOP FIVE<br />KAREN LOPEZ B.<br />
2. 2. A conjecture is a proposition that is unproven but appears correct and has not been disproven. After demostrating the truth of a conjecture, this came to be considered a theorem and as such can be used to build other formal proofs.<br />
3. 3. Given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color.<br />5. FOUR COLOR THEOREM <br />STATEMENT<br />Example<br />
4. 4. There is a prime number between n2 and (n + 1)2 for every positive integer n. <br />n=1<br /> Between 1 and 4 are 2 and 3<br />n=2<br /> Between 4 and 9 are 5 and 7<br />n=3<br /> Between 9and 16 are 11 and 13<br />4. LEGENDRE’S CONJECTURE <br />STATEMENT<br />Examples<br />
5. 5. There are infinitely many primes p such that p+2 is also prime.<br />3. Conjecture twin prime numbers<br />STATEMENT<br />Examples<br /> p = 3 and p+2 = 5<br /> p = 5 and p+2 = 7<br /> p = 11 and p+2 = 13<br /> p = 29 and p+2 = 31<br />
6. 6. Every even integer greater than 2 can be expressed as the sum of two primes.<br /> 4 = 2+2<br />6 = 3+3<br />8 = 3+5<br />10 = 3+7 = 5+5<br />2. Goldbach’s Conjecture<br />Examples<br />STATEMENT<br />
7. 7. No there positive integers a, b and c, can satisfy the equation an + bn = cn for any integer value of n greater than two.<br />For n=2 <br />a=3 b=4 c=5<br />then<br />32 + 42 = 52<br />1. fermat’s last theorem<br />STATEMENT<br />Example<br />
8. 8. « I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it. »<br />Pierre de Fermat[, 1637<br />