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

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1.	Find all congruent solutions of `8x -= 6` (mod 14).
Answer» Given, `8x -= 6` (mod 14) `therefore lambda=(8x-6)/(14)`, where `lambdainI_(+)` `therefore 8x=14lambda+6` `implies x=(14lambda+6)/(8)` `implies x=(7lambda+3)/(4)` `=(4lambda+3(lambda+1))/(4)` `x=lambda+(3)/(4)(lambda+1)`,where `lambdainI_(+)` and here greatest common divisor of 8 and 14 is 2, so there are two required solutions. For `lambda = 3` and 7, x = 6 and 13.

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