P1

Part of 2024 Bangladesh Mathematical Olympiad

Problems(2)

Easy diophantine equation

Source: BdMO 2024 Secondary National P1

Find all non-negative integers

x, y

x^3y+x+y=xy+2xy^2

Diophantine equationnumber theoryDivisibilityfactorization

Source: BdMO 2024 Higher Secondary National P1

Find all prime numbers

p

q

p^3-3^q=10.

Proposed by Md. Fuad Al Alam

number theoryDiophantine equationmodular arithmeticprime numbers