Question

Find least positive integer x
satisfying 276x + 128 = 4 (mod 7)
[Hint : 276 = 3, 128 = 2 (mod 7)]​

Answer 1

Given: The expression 276x + 128 = 4 (mod 7)

To find: The least positive integer x.

Solution:

• Now we have given the expression:

                   276x + 128 = 4 (mod 7)    

• Now we have given the value of

                   276 / 7 = 3 and 128 / 7 = 2

• Consider LHS, we gave:

                   276x + 128             ...............(i)

• Now we will divide (i) by 7, we get:

                   276x + 128 / 7

                   276x / 7 + 128 / 7

• Now substituting the values, we get:

                   3(mod 7) × x(mod 7) + 2(mod 7)

• Now comparing this with RHS, we get:

                   (3x + 2)(mod 7) = 4 (mod 7)

• Now when we will divide 3x + 2 by 7, the remainder should be 4.

• So:

                   3(3) + 2 / 7 = 4

                   x = 3

Answer:

              So the least positive integer is 3.