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Find all congruent solutions of 8x -= 6 ...

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

A

[8],[6]

B

[8],[14]

C

[6],[13]

D

[8],[14],[16]

Text Solution

Verified by Experts

The correct Answer is:
C
`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]
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