Problem 3

Part of 2021 Brazil Undergrad MO

Problems(1)

Almost Square-minus-constant

Source: Brazilian Undergrad MO 2021 Problem 3

Find all positive integers

k

for which there is an irrational

\alpha>1

and a positive integer

N

\left\lfloor\alpha^{n}\right\rfloor

m^2-k

m \in \mathbb{Z}

for every integer

n>N

Brazilian Undergrad MO 2021real analysispowersirrational numberapproximationPerfect Square