6

Part of 2024 CAPS Match

Problems(1)

every prime p divides floor(a+b*sqrt(2024)^p)-c

Source: CAPS 2024 p6

Determine whether there exist infinitely many triples

(a, b, c)

of positive integers such that every prime

p

\left\lfloor\left(a+b\sqrt{2024}\right)^p\right\rfloor-c.

combinatoricsnumber theoryinternational competitionsCombinatorial Number Theoryprime numberstripletspositive integers