MathDB

For

a,n

positive integers we show number of different integer 10-tuples

(x_1,x_2,...,x_{10})

(mod n)

satistfying

x_1x_2...x_{10}=a (mod n)

with

f(a,n)

. Let

a,b

given positive integers , a) Prove that there exist a positive integer

c

such that for all

n\in \mathbb{Z^+}

\frac {f(a,cn)}{f(b,cn)}

is constant b) Find all

(a,b)

pairs such that minumum possible value of

c

is 27 where

c

satisfying condition in

(a)

Problem Statement