MathDB

N3

Part of 2016 Costa Rica - Final Round

Problems(2)

diophantine 3 x 2^a + 1 = b^2

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N3 day1

9/23/2021
Find all nonnegative integers aa and bb that satisfy the equation 3⋅2a+1=b2.3 \cdot 2^a + 1 = b^2.
number theoryDiophantine equationdiophantine
(n -1)2^{n - 1} + 5 = m^2 + 4m

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N3 day2

9/24/2021
Find all natural values of nn and mm, such that (n−1)2n−1+5=m2+4m(n -1)2^{n - 1} + 5 = m^2 + 4m.
Diophantine equationdiophantinenumber theory