Question 1209950
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The function f(n) takes the integers to the real numbers such that
f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn
for all integers m and n, and f(1) = 2.  Find f(n).
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The solution by @CPhill,  producing the formula   f(n) = {{{(n^3 + 7n^2)/4}}}   as the final answer,  is  INCORRECT.


It is seen even by an disarmed eye,  since the basic formula in the post


          f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn


must generate  INTEGER  values for positive integer  m  and  n,  which is clear by induction.



On the contrary,  the formula    f(n) = {{{(n^3 + 7n^2)/4}}}    by @CPhill produces  
fractional numbers for every second odd integer number.



This  CONTRADICTION  kills/disproves the solution and the answer by  @CPhill to the death.