And the subheading should suggest what's coming...

Can we find a base in which 21 can be divided by 12 without remainder? And why should we? - Because someone said it couldn't be done. They may well have meant that it can't be done if the base is a positive number - and in fact, if you use base (-5) then 21 = 3 x 12 is true.

Which led me to look at some other results in other bases - not recent discoveries, I might add; the keyboard is ready and willing to work, but occasional bursts of lethargy often hit the typist, in particular Nap Attacks as favoured by Garfield.¹

31 = 2 x 13 (base 5)
41 = 3 x 14 (base eleven)
51 = 3 x 15 (base seven)
51 = 4 x 15 (base nineteen)

In tabular form:

Number	Bases
31	5
41	11
51	7, 19
61	29
71	9, 17, 41
81	13, 55
91	11, 31, 71
T1	23, 89
E1	13, 19, 29, 49
and here are some with 2 as unit-figure
52	8
72	19
82	11
92	34
T2	19
E2	14, 53

and so on ...
(to be continued)