For each of the following congruences, find all integers N, with N>1, that make the congruence true. 6equiv60(mod N).

Question

For each of the following congruences, find all integers N, with N>1, that make the congruence true.

6 \equiv 60 (m o d N)

.

Answer 1

Concept used:

x \equiv y (m o d n)

if and only if x and y differ by a multiple of n.
The given congruence is,

6 \equiv 60 (m o d N)

.
The difference of the given congruence integers is calculated as,

x - y = 6 - 60 = - 54

The factors of -54 for N > 1 are 2,3, 6,9, 18, 27 and 54 , so the integers for the given congruences are 2, 3, 6,9, 18,27 and 54.
Thus, the integers for the given congruences are 2,3, 6,9, 18, 27 and 54.

For each of the following congruences, find all integers N, with N>1, that make the congruence true. 6equiv60(mod N).

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