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Real equation (Posted on 2020-10-11) Difficulty: 3 of 5
Find all functions f:R->R satisfying the equality f(f(x)+f(y))=(x+y)f(x+y) for all real x and y.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts First thoughts Comment 1 of 1
At first glance, it seems to me that the function must be a polynomial. 

If the polynomial is of order n, then the LHS is of order n^2 and the RHS is of order n + 1.  This rules out most functions, in my mind.

Only f(x) = 0 seems to work.

I will be very interested to see if anybody comes up with anything else.

  Posted by Steve Herman on 2020-10-11 14:52:00
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