Difference between revisions of "1982 AHSME Problems/Problem 20"
LOTRFan123 (talk | contribs) (Created page with "==1982 AHSME Problems/Problem 20== ==Problem== The number of pairs of positive integers <math>(x,y)</math> which satisfy the equation <math>x^2+y^2=x^3</math> is <math>\tex...") |
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− | 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