"Find all whole number solutions of the congruence..." solved and explained

Nola Aguilar

Answered question

2022-11-21

Find all whole number solutions of the congruence equation.

(2 x + 1) \equiv 5 mod 4

Eva Cochran

Beginner2022-11-22Added 14 answers

Given,

(2 x + 1) \equiv 5 mod 4

To find a whole number x<4, such that

\frac{2 x + 1 - 5}{4}

is an integer.
if

x = 0, = \frac{- 4}{4} = - 1

is an integer.
if

x = 1, = \frac{- 2}{4}

if x=2, =0 is an integer.
if

x = 3, = \frac{2}{4}

Hence, the whole number solutions of the given congruence equation are x,(x+4),x+(2*4),...
0,2,4,6,8,..
Result:
0,2,4,6,8,...

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