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pow:problem2f20 [2020/09/30 00:47] mazur |
pow:problem2f20 [2020/10/01 00:16] (current) mazur |
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+ | <box 80% round orange|Problem 2 (due Monday, September 28)> | ||
+ | Let $\mathbb N_0$ be the set $\{0,1,2,\ldots\}$ of all non-negative integers. Find all functions $f:\mathbb N_0 | ||
+ | \longrightarrow \mathbb N_0$ such that $f(a^2+b^2)=f(a)^2+f(b)^2$ for all $a,b$ in $\mathbb N_0$. | ||
+ | </box> | ||
+ | No complete solution was received. Partial solutions submitted by Yuqiao Huang, Maxwell T Meyers, and | ||
+ | Matthew Pressimone. Detailed solution is discussed in the following link {{:pow:2020fproblem2.pdf|Solution}} |