Question

7x≡1(mod26)?

Answer 1

\(\large \mathbb{7x \equiv 1 \mod 13*2}\)

Answer 2

\(\large \mathbb{7x \equiv 1 \mod 2}\)
\(\large \mathbb{7x \equiv 1 \mod 13}\)

Answer 3

\(\large \mathbb{7x \equiv 1 \mod 2}\)

\(\large \mathbb{\implies x \equiv 1 \mod 2}\)
\(\large \mathbb{\implies x = 2k+1}\)

Answer 4

\(\large \mathbb{7x \equiv 1 \mod 13}\)

\(\large \implies 7(2k+1) \equiv 1 \mod 13\)

\(\large \implies 14k+7 \equiv 1 \mod 13\)

\(\large \implies k+7 \equiv 1 \mod 13\)

\(\large \implies k \equiv 7 \mod 13\)

\(\large \implies k = 13m + 7\)

Answer 5

substitute this \(k\) value in first equation for \(x\) :

\(\large \mathbb{x = 2k+1 = 2(13m+7)+1 = 26m + 15}\)

\(\large \mathbb{x \equiv 15 \mod 26} \)