Consecutive Diophantine Equation
Number Theory
Level
5
Find the number of ordered integral solutions (x,y) of the diophantine equation:
y(y+1) = x(x+1)(x+2)
Note: The problem is not original. Taken from "Introductory Algebraic Number Theory" by Alaca and Williams.
The answer is 10.
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1 solution
Calculate roots of the quadratic equation: y 2 + y − x ( x + 1 ) ( x + 2 ) = 0