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FAMOUS CONJECTURE
S
TOP FIVE
KAREN LOPEZ B.
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.
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
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 9 and 16 are 11
and 13
4. LEGENDRE’S CONJECTURE
STATEMENT
Examples
There are infinitely
many primes p such
that p+2 is also
prime.
p = 3 and p+2 =
5
p = 5 and p+2 =
7
p = 11 and p+2 =
13
p = 29 and p+2 =
31
3. CONJECTURE TWIN PRIME NUMBERS
STATEMENT Examples
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
STATEMENT Examples
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
« 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