MathDB

1

Part of 1991 Iran MO (2nd round)

Problems(2)

On the equation x+x^2=y+y^2+y^3 [Iran Second Round 1991]

Source:

11/29/2010
Prove that the equation x+x2=y+y2+y3x+x^2=y+y^2+y^3 do not have any solutions in positive integers.
number theory proposednumber theory
Six points with rational coordinates[Iran Second Round 1991]

Source:

11/30/2010
Prove that there exist at least six points with rational coordinates on the curve of the equation y3=x3+x+13701370y^3=x^3+x+1370^{1370}
analytic geometryalgebra proposedalgebra