MathDB

For each

1\leq i\leq 9

and

T\in\mathbb N

, define

d_i(T)

to be the total number of times the digit

i

appears when all the multiples of

1829

between

1

and

T

inclusive are written out in base

10

.
Show that there are infinitely many

T\in\mathbb N

such that there are precisely two distinct values among

d_1(T)

d_2(T)

\dots

d_9(T)

N5