MathDB

Is this function periodic?

Source: Turkey TST 2021 D-3, P-2

May 21, 2021

algebrafunctional equationfunction

Problem Statement

Let

c

be a real number. For all

x

and

y

real numbers we have,

f(x-f(y))=f(x-y)+c(f(x)-f(y))

and

f(x)

is not constant.

a)

Find all possible values of

c

.

b)

Can

f

be periodic?

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