for every , ,
for this case, just use definition (b)
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).
That said, both MathWorld and Planet Math use (a), and Planet Math specifies that . If I am not mistaken, both definitions are equivalent if .
I agree with the OP's assessment of "a is congruent to a mod 0".