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--- pow:problem2f24 [2024/09/23 17:54] – created mazur
+++ pow:problem2f24 [2024/09/24 04:22] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange|Problem 2 (due on Monday, September 23) >
+Let $f:\mathbb R\longrightarrow \mathbb R$ be a function such for any $x,y$ either
+$f(x-y)+f(y)=f(x)$ or $f(y-x)+f(x)=f(y)$. Prove that the sum $f(x)+f(-x)$ assumes at most two different
+values. Find an example when $f(x)+f(-x)$ assumes two different values.
+</box>
+We received two solutions (one partial and one complete), from Levi Axelrod and Surajit Rajagopal.
+Levi's solution is similar to our solution and the example he provided is simpler than the one
+in our original solution. For a detailed solution see the following link {{:pow:2024fproblem2.pdf|Solution}}.