# Thread: [SOLVED] congruent modulo n

1. ## [SOLVED] congruent modulo n

For the statement "a is congruent to b modulo n"
Which of the following definition is correct.

a) a - b is divisible by n.

b) a - b is a multiple of n.

or whether both are acceptable.

Whether "a is congruent to a mod 0" is true?

a - a = 0 is divisible by 0 is wrong. But 0 is a multiple of 0 is correct. So whether to consider
the definition (a) or definition (b).

2. for every $\displaystyle a \in \mathbb{R}$, $\displaystyle a = a + k(0)$, $\displaystyle k \in \mathbb{N}$
so $\displaystyle a \equiv a ~mod ~0$.

for this case, just use definition (b)

regards

3. Originally Posted by sudeepmansh
For the statement "a is congruent to b modulo n"
Which of the following definition is correct.

a) a - b is divisible by n.

b) a - b is a multiple of n
The correct answer: in mathematics, it is not customary to argue about definitions.

That said, both MathWorld and Planet Math use (a), and Planet Math specifies that $\displaystyle n\ne 0$. If I am not mistaken, both definitions are equivalent if $\displaystyle n\ne 0$.

I agree with the OP's assessment of "a is congruent to a mod 0".