Ciro Santilli @cirosantilli 37

They are apparently provided upon request as per various whatdotheyknow.com links, so it is quite stupid that they don't just publicly provide them therefore.

If there are infinitely many inputs, we can always construct a (potentially exponentially huge) Turing machine that hardcodes the outcome for every possible input, so the problem is never undecidable.

The problem is of course deciding and proving the outcome for each possible input, notably as it is possible that calculation for some of the inputs may be independent from ZFC.

Very focused on the International Mathematical Olympiad, notably they maintain all solutions at: artofproblemsolving.com/wiki/index.php/IMO_Problems_and_Solutions

en.wikipedia.org/w/index.php?title=Farey_sequence&oldid=1223364653#Sequence_length_and_index_of_a_fractionwhere $\Phi (n)$ is the totient summatory function.

Company founded by Marc Verdiell in his garage, and later acquired by Intel which was going on a optoelectronics buying spree. The division was later sold off in 2023 of course during more difficult times: www.theregister.com/2023/10/31/intel_silicon_photonics_jabil/

On Crunchbase: www.crunchbase.com/organization/lightlogic

It's hard to understand exactly what the company did by Googling it nowadays. Sad and usual fate. Presumably something related to transceiver for fiber-optic communication. Only the patents remain: patents.google.com/?assignee=lightlogic&oq=lightlogic to tell its story to the brave.

www.quora.com/Is-MIT-the-only-place-where-homework-is-called-problem-sets
Terminology by location:
Places that say "problem set":Places that say "problem sheet":Places that say "example sheet":

Ciro Santilli's take on it: Section "Give answers".

A "reduced fraction" is a fraction that has the smallest possible integer numerator and denominator for its value.

For example:is not a reduced fraction, because there is another fraction equal to it but with smaller numerator and denominator: