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Question Number 55358 by gunawan last updated on 22/Feb/19

$$\mathrm{Determine}\mathrm{all}\mathrm{functions}f:\mathbb{N}\to \mathbb{N}$$$$\mathrm{satisfying}$$$$xf\left(y\right)+yf\left(x\right)=(x+y)f(x^2+y^2)$$$$\mathrm{for}\mathrm{all}\mathrm{positive}\mathrm{integers}x\mathrm{and}y$$

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