Difference between revisions of "1982 AHSME Problems/Problem 20"
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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: \text{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> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME box|year=1982|num-b=19|num-a=21}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 01:54, 30 June 2025
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 
See Also
| 1982 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
