Question

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

Congruence
ANSWERED
asked 2020-12-21
For each of the following congruences, find all integers N, with N>1, that make the congruence true.
\(23\equiv13(mod\ N)\).

Answers (1)

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.
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