Famous conjectures
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Famous conjectures

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Famous conjectures Presentation Transcript

  • 1. Famous conjectures
    TOP FIVE
    KAREN LOPEZ B.
  • 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.
  • 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.
    5. FOUR COLOR THEOREM
    STATEMENT
    Example
  • 4. There is a prime number between n2 and (n + 1)2 for every positive integer n.
    n=1
    Between 1 and 4 are 2 and 3
    n=2
    Between 4 and 9 are 5 and 7
    n=3
    Between 9and 16 are 11 and 13
    4. LEGENDRE’S CONJECTURE
    STATEMENT
    Examples
  • 5. There are infinitely many primes p such that p+2 is also prime.
    3. Conjecture twin prime numbers
    STATEMENT
    Examples
    p = 3 and p+2 = 5
    p = 5 and p+2 = 7
    p = 11 and p+2 = 13
    p = 29 and p+2 = 31
  • 6. Every even integer greater than 2 can be expressed as the sum of two primes.
    4 = 2+2
    6 = 3+3
    8 = 3+5
    10 = 3+7 = 5+5
    2. Goldbach’s Conjecture
    Examples
    STATEMENT
  • 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.
    For n=2
    a=3 b=4 c=5
    then
    32 + 42 = 52
    1. fermat’s last theorem
    STATEMENT
    Example
  • 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. »
    Pierre de Fermat[, 1637