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5

Part of 2022 ISI Entrance Examination

Problems(1)

B.Stat & B.Math 2022 - Q5

Source: Indian Statistical Institute (ISI) - B.Stat & B.Math Entrance 2022

5/8/2022
For any positive integer nn, and i=1,2i=1,2, let fi(n)f_{i}(n) denote the number of divisors of nn of the form 3k+i3 k+i (including 11 and nn ). Define, for any positive integer nn, f(n)=f1(n)−f2(n)f(n)=f_{1}(n)-f_{2}(n) Find the value of f(52022)f\left(5^{2022}\right) and f(212022)f\left(21^{2022}\right).
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