Find the whole number sulotion of the congruence

Julieve Vega

Julieve Vega

Answered question

2022-05-07

Find the whole number sulotion of the congruence equation of (5x+4)=2 mod 8

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-05Added 106 answers

The given congruence equation is:
5x+42(mod8)
We want to find the whole number solutions for this congruence equation.
First, let's simplify the left-hand side of the congruence equation:
5x+42(mod8)
5x24(mod8)
5x2(mod8)
Next, we need to find the multiplicative inverse of 5 modulo 8, denoted as 51. This is the number such that 5×511(mod8).
To find 51, we can use the extended Euclidean algorithm as follows:
8=5×1+3
5=3×1+2
3=2×1+1
1=32×1
=3(53×1)×1
=2×35
=2×(85)5
=5×2+8
512(mod8)
Now we can multiply both sides of the congruence equation by 51:
5x2(mod8)
51×5x51×2(mod8)
x10(mod8)
x6(mod8)
Therefore, the whole number solution for the congruence equation 5x+42(mod8) is x6(mod8).

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