MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1999 National Olympiad First Round
28
28
Part of
1999 National Olympiad First Round
Problems
(1)
Function
Source: 0
4/21/2009
Find the number of functions defined on positive real numbers such that f\left(1\right) \equal{} 1 and for every
x
,
y
∈
ℜ
x,y\in \Re
x
,
y
∈
ℜ
, f\left(x^{2} y^{2} \right) \equal{} f\left(x^{4} \plus{} y^{4} \right).
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1
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2
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4
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Infinitely many
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}
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0
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1
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2
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4
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Infinitely many
function
trigonometry