MathDB

4

Part of 2008 Hanoi Open Mathematics Competitions

Problems(2)

diophantine m^2 + n^2 = 3(m + n) (HOMC 2008 J Q4)

Source:

7/25/2019
Find all pairs (m,n)(m,n) of positive integers such that m2+n2=3(m+n)m^2 + n^2 = 3(m + n).
number theoryDiophantine equationdiophantine
HOMC 2008 P4

Source: HOMC 2008, Vietnam

3/10/2016
Prove that there exists an infinite number of relatively prime pairs (m,n)(m, n) of positive integers such that the equation x3āˆ’nx+mn=0x^3-nx+mn=0 has three distint integer roots.
homcalgebranumber theoryequationrelatively prime