Find all congruent solutions of `8x -= 6` (mod 14).

Options

A. [8],[6]
B. [8],[14]
C. [6],[13]
D. [8],[14],[16]

Answer

C

Explanation

`lambda=(8x-6)/(14), "where "lambda in I_(+)`
`therefore 8x=14lambda+6impliesx=(14lambda+6)/(8)`
`implies x=(7lambda+3)/(4)=lambda+(3)/(4)(lambda+1),"where "lambda in I` and here greatest common divisor of 8 and 14 is 2, so there are two required solutions. for `lambda = 3 and lambda = 7, x = 6, 13` or x = [6][13]