CAT 2019 Functions Question (Hard)

Question

Let f be a function such that f mn f m f n for every positive integers m and n. If f 1 , f 2 and f 3 are positive integers, f 1 f 2 , and f 24 54, then f 18 equals TITA

Accepted Answer

We are given for all positive integers . are positive integers with . . We must find . --- Step 1 Value of Set in the functional equation f 1 cdot n f 1 f n implies f n f 1 f n Hence since . --- Step 2 Prime factorization approach The function is completely multiplicative f 24 f 2 3 cdot 3 f 2 3 cdo

CAT 2019

Quantitative

Functions

Hard

$Let f be a function such that f(mn) = f(m) f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then f(18) equals [TITA]$

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