64 (number) 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number that is both a perfect square and a perfect cube. Since
Proof that π is irrational be 0, because otherwise it would follow from claim 1 that each "f"("x") ("n" ∈ N) would be 0, which would contradict claim 2. Now, take a natural number "c" such that all three numbers "bc"/"k", "ck"/"x" and "c"/"x" are integers and consider the sequence Then On the other hand, it follows from claim 1 that which is a linear combination of "g" and "g" with integer coefficients. Therefore, each "g" is an integer multiple of "y". Besides, it follows from claim 2 that each "g" is greater than 0 (and therefore that "g" ≥ |"y"|) if "n" is large