Kuznetsova equation

Kuznetsova equation refers to problem below.

Find integer \( A,B,C \) such that

for any non-negative integer \( n \) there exist integer \( m \) such that

\( A^{B n + C} = B m+ C \)

Example of solution:

\( A=3 \) \( B=100 \) \( C=87 \)