5

Part of 1999 South africa National Olympiad

Problems(1)

Denominators are powers of 3

Source: South Africa 1999

S

be the set of all rational numbers whose denominators are powers of 3. Let

a

b

c

be given non-zero real numbers. Determine all real-valued functions

f

that are defined for

x \in S

f(x) = af(3x) + bf(3x - 1) + cf(3x - 2) \textrm{ if }0 \leq x \leq 1,

and are zero elsewhere.

functionnumber theory unsolvednumber theory