For each of the following congruences, find all integers N, with N&gt;1, that make the congruence true. 6≡60(mod N).

Concept used: x≡y(mod n) if and only if x and y differ by a multiple of n. The given congruence is, 6≡60(mod N). The difference of the given congruence integers is calculated as, x−y=6−60=−54 The factors of -54 for N &gt; 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.

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High School
Geometry
High school geometry
Congruence

remolatg

Answered question

2020-12-13

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 & Explanation

FieniChoonin

Skilled2020-12-14Added 102 answers

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.

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