# Prove that a necessary and sufficient condition for a non negative integer n to be divisible by a positive integer d is that n mod d = 0?

• Prove that a necessary and sufficient condition for a non negative integer n to be divisible by a positive integer d is that n mod d = 0?

Answer #1 | 15/11 2015 10:12
d|n ⇔ n ≡ 0 mod d d|n ⇔ n=kd+0 for some positive integer k ⇔ n-0 is a multiple of d ⇔ n ≡ 0 mod d
Positive: 50 %
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Answer #9 | 15/11 2015 18:12
d|n ⇔ n ≡ 0 mod d d|n ⇔ n=kd+0 for some positive integer k ⇔ n-0 is a multiple of d ⇔ n ≡ 0 mod d
Positive: 0 %