# Difference between revisions of "1982 AHSME Problems/Problem 20"

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==Solution== | ==Solution== | ||

− | Rearrange the equation to <math>y^2=x^3-x^2=x^2(x-1)</math>. This equation is satisfied whenever <math>x-1</math> is a perfect square. There are infinite possible values of <math>x</math>, and thus the answer is <math>\boxed{D: Not Finite}</math> | + | Rearrange the equation to <math>y^2=x^3-x^2=x^2(x-1)</math>. This equation is satisfied whenever <math>x-1</math> is a perfect square. There are infinite possible values of <math>x</math>, and thus the answer is <math>\boxed{D: \text{Not Finite}}</math> |

## Latest revision as of 13:15, 22 August 2015

## 1982 AHSME Problems/Problem 20

## Problem

The number of pairs of positive integers which satisfy the equation is

## Solution

Rearrange the equation to . This equation is satisfied whenever is a perfect square. There are infinite possible values of , and thus the answer is