To solve: The congruence 3x\equiv 5(\bmod 7)

Mylo O'Moore

Mylo O'Moore

Answered question

2021-03-22

To solve:
The congruence 3x5(bmod7)

Answer & Explanation

stuth1

stuth1

Skilled2021-03-24Added 97 answers

To solve the congruence 3x5(bmod7), try each of the numbers
0, 1, 2,3, 4, 5 and 6 to see which one solves the congruence.
For x=0
3×05(bmod7), but it is not true since 3×00(bmod7). So, x = 0
is not the solution of the given congruence.
For x=1
3×1=5(bmod7).
35(bmod7), butit is not true since 33(bmod7). So, x = 1 is
not the solution of the given congruence.
For x=2
3×25(bmod7).
65(bmod7), but it is not true since 66(bmod7). So, x = 2 is
not the solution of the given congruence.
For x =3
3×35(bmod7).
95(bmod7), but it is not true since 92(bmod7). So, x = 3 is
not the solution of the given congruence.
For x=4
3×45(bmod7).
125(bmod7), and itis true. So, x = 4 is the solution of the
given congruence.
Thus, x = 4 is the solution of the given congruence 3x5(bmod7)
Final Statement:
Therefore, the solution of the congruence 3x5(bmod7)isx=4.

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