# math – update

## #23: The Prime Theorem of Math = The Prime Number Theorem

Q: Did you ever realized that the Prime Number Theorem is equivalent to the statement that the nth prime number pn satisfies

## Day #11: Mighty Infinitude of Primes

Q: Could you too prove one of the most important results in Number Theory and Mathematics: The infinitude of prime numbers??… Continue reading

## Day #10: ABC Conjecture

Shinichi Mochizuki

Q: Can you see the equivalence of the three following statements of the ABC conjecture??…

ABC Conjecture I. For every ε > 0, there exist only finitely many triples (a, b, c) of coprime positive integers, with a + b = c, such that:

ABC Conjecture II. For every ε > 0, there exists a constant Kε such that for all triples (a, b, c) of coprime positive integers, with a + b = c:

ABC Conjecture III. For every ε > 0, there exist only finitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1 + ε.

## Day #6: Perfect Numbers, Perfect Friends, Perfect S(.)X!

Q: Number 6 is a Perfect Number!!… Can you give a geometric proof of this wonderful fact??…

## Day #5: From Pythagoras to the Mathematics of the 3rd Millennium

Q: Could you give at least 10 more proofs of the Pythagorean Theorem, and state how it is related to todays most actual mathematics and the most famous mathematical problem of all times??…

## Day #:2 Craziness of the Square Roots of Primes!

Q: Could you give a proof of the irrationality of the square root of Your favorite prime number p??…