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--- pow:problem6f23 [2023/11/21 08:11] – mazur
+++ pow:problem6f23 [2023/11/21 08:13] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 6 (due Monday, November 20)>
+Find all bounded continuous functions $f:\mathbb R\longrightarrow \mathbb R$ which satisfy the following condition:
+\[ f^2(x)-f^2(y)=f(x+y)f(x-y)\ \ \text{for all $x,y\in \mathbb R$}.\]
+Here $f^2=f\cdot f$ is the square of the function $f$ (and not the composition of $f$ with itself).
+</box>
+We received two attempts at solving the problem, both far from being correct. The functions which satisfy the conditions
+of the problem are exactly all functions of the form $f(x)=A\sin bx$ for some real numbers $A,b$. For detailed
+solutions (we have two) see the following link {{:pow:2023fproblem6.pdf|Solution}}.