Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod

d.

Question

Hugh Pruitt

Mathematics

23 April, 15:48

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod

d.

+3

Answers (1)

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Chum · Answer 1

From the rules of modular arithmetic, (A+B) mod C = (A) modC + (B) modC

So, (m + dk) mod d = (m) mod d + (dk) mod d

clearly (dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.

Thus

(m + dk) mod d = (m) mod d + (dk) mod d = (m) mod d + 0 = (m) mod d

(m + dk) mod d = (m) mod d

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m modd.

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod

d.