Talk:Congruence of Sum of Digits to Base Less 1

Can't we simply say:

\(\ds x\)

\(=\)

\(\ds \sum_{j \mathop = 0}^m r_j b^j\)

Basis Representation Theorem

\(\ds \)

\(\equiv\)

\(\ds \sum_{j \mathop = 0}^m r_j 1^j\)

\(\ds \pmod {b - 1}\)

Congruence of Powers

\(\ds \)

\(\equiv\)

\(\ds \sum_{j \mathop = 0}^m r_j\)

\(\ds \pmod {b - 1}\)

\(\ds \)

\(\equiv\)

\(\ds \map {s_b} x\)

\(\ds \pmod {b - 1}\)

Definition of Digit Sum

By the way, this theorem proves Digital Root is Congruent to Number Modulo Base minus 1 after induction. --RandomUndergrad (talk) 08:59, 23 February 2022 (UTC)

Yes I knew it was somewhere, I couldn't find it. --prime mover (talk) 18:36, 23 February 2022 (UTC)