1994 AIME Problems/Problem 7

Revision as of 22:46, 15 September 2023 by Nnbabu (talk | contribs) (Solution)

Problem

For certain ordered pairs $(a,b)\,$ of real numbers, the system of equations

$ax+by=1\,$
$x^2+y^2=50\,$

has at least one solution, and each solution is an ordered pair $(x,y)\,$ of integers. How many such ordered pairs $(a,b)\,$ are there?

Solution

bro whoever came up with this problem must've been drunk tbh, there are literally infinite solutions...

See also

1994 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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