MathDB

6

Part of 2017 Hanoi Open Mathematics Competitions

Problems(2)

diophantine with prime p, 2^mp^2 + 27 = q^3 (HOMC 2017 J Q6)

Source:

8/7/2019
Find all triples of positive integers (m,p,q)(m,p,q) such that 2mp2+27=q32^mp^2 + 27 = q^3 and pp is a prime.
number theoryDiophantine equationprimediophantine
2-parameter diophantine system (HOMC 2017 S Q6)

Source:

9/8/2019
Find all pairs of integers a,ba, b such that the following system of equations has a unique integral solution (x,y,z)(x , y , z ) : {x+y=a−1x(y+1)−z2=b\begin{cases}x + y = a - 1 \\ x(y + 1) - z^2 = b \end{cases}
Diophantine Equationsdiophantinesystem of equationsnumber theoryparametric equation