MathDB

B.Stat & B.Math 2022 - Q5

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

May 8, 2022

isiIndian Statistical Institutenumber theory2022

Problem Statement

For any positive integer

n

, and

i=1,2

, let

f_{i}(n)

denote the number of divisors of

n

of the form

3 k+i

(including

1

and

n

). Define, for any positive integer

n

f(n)=f_{1}(n)-f_{2}(n)

Find the value of

f\left(5^{2022}\right)

and

f\left(21^{2022}\right)