MathDB
Function

Source: 0

April 21, 2009
functiontrigonometry

Problem Statement

Find the number of functions defined on positive real numbers such that f\left(1\right) \equal{} 1 and for every x,y x,y\in \Re, f\left(x^{2} y^{2} \right) \equal{} f\left(x^{4} \plus{} y^{4} \right).
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 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}