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(#M40022011) MATHS OLYMPIAD question ALGEBRA Keep an EYE

Let f : Z ! Z be a function satisfying f(0) = 0, f(1) = 0 and
(i) f(xy) + f(x)f(y) = f(x) + f(y);
(ii)f(x y) − f(0)


f(x)f(y) = 0,
for all x, y 2 Z, simultaneously.
(a) Find the set of all possible values of the function f.
(b) If f(10) 6= 0 and f(2) = 0, find the set of all integers n such that
f(n) 6= 0

Asked In Maths Olympiad MAN (10 years ago)

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