MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2009 National Olympiad First Round
16
16
Part of
2009 National Olympiad First Round
Problems
(1)
x+19y = 0 mod 23 and x+y < 69
Source: 0
4/28/2009
x \plus{} 19y \equiv 0 \pmod {23} and x \plus{} y < 69. How many pairs of
(
x
,
y
)
(x,y)
(
x
,
y
)
are there in positive integers?
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A
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100
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102
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C
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105
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109
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None
<span class='latex-bold'>(A)</span>\ 100 \qquad<span class='latex-bold'>(B)</span>\ 102 \qquad<span class='latex-bold'>(C)</span>\ 105 \qquad<span class='latex-bold'>(D)</span>\ 109 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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100
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102
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105
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109
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E
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None
modular arithmetic