The first ten digits of \( \pi \) after the decimal point
are \( 3.1415926535 \)
The positive real solution to the equation
\( 242x^4+113x-23928=0 \)
to ten decimal places is \( 3.1415926535 \)
They must be the same number. Are they? Surely \( \pi \) must be a solution to this equation.
The numbers which are 0 or 2 mod 5 are
0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, ...
The sequence of numbers \( \lfloor n \sqrt{2 \pi} \rfloor \)
for \(n=0,1,2,3,...\) is
0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, ...
Are these sequences always equal? Surely they must be the same sequence.