Question

# For each of the following congruences, find all integers N, with N>1, that make the congruence true. 23equiv13(mod N).

Congruence
For each of the following congruences, find all integers N, with N>1, that make the congruence true.
$$23\equiv13(mod\ N)$$.

2020-12-22
Concept used:
$$x \equiv y(mod\ n)$$ if and only if x and y differ by a multiple of n.
The given congruence is,
$$23\equiv 13(mod\ N)$$.
The difference of the given congruence integers is calculated as,
$$x-y=23-13=10$$
The factors of 10 for N > 1 are 2,5, and 10 , so the integers for the given congruences are 2,5, and 10.
Thus, the integers for the given congruences are 2,5, and 10.