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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1997 AMC 12/AHSME
28
28
Part of
1997 AMC 12/AHSME
Problems
(1)
Ordered Triples of Integers Satisfying Two Equations
Source:
1/18/2009
How many ordered triples of integers
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
satisfy|a \plus{} b| \plus{} c \equal{} 19 \text{and} ab \plus{} |c| \equal{} 97?
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4
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6
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10
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<span class='latex-bold'>(A)</span>\ 0\qquad <span class='latex-bold'>(B)</span>\ 4\qquad <span class='latex-bold'>(C)</span>\ 6\qquad <span class='latex-bold'>(D)</span>\ 10\qquad <span class='latex-bold'>(E)</span>\ 12
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4
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6
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10
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12