#! /usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

use List::Util qw{ sum };
for my $A (2..20) {
    for my $n (1..10) {
        die "$A, $n\n"
            unless $A ** $n == 1 + ($A - 1) * sum(map $A ** $_, 0 .. $n - 1)
    }
}