The general solution of the congruence 98x – 1 ≡ 0 (mod 139) is ____.

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Detailed Solution

The congruence 98x – 1 = 0(mod 139)
means that 98x−1 is divisible by 139
If y is the quotient, then 98x – 1 = 139y, or 98x − 139y = 1
If

13998

is converted into a continued fraction the convergent just preceding the fraction is

6143

.
Hence, the general solution of the equation is
x = 61 + 139t, y = 43 + 98t
The general solution of the congruence 98x – 1 ≡ 0 (mod 139) is x = 61 + 139t, y = 43 + 98t.

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