Can someone please help me on this problem in modular Arithmetic Congruences I ran into this problem on aops alcumus
If $3x+7\equiv 2\pmod{16}$, then $2x+11$ is congruent $\pmod{16}$ to what integer between $0$ and $15$, inclusive?
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Hint: $6 \cdot 3 \equiv 2 \bmod 16$
lhf
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1i.e. as here, scale the first congruence by $,\dfrac{\color{#0a0}2}{\color{#c00}3}\equiv \dfrac{18}3\equiv 6,$ to change the coef of $x$ from $,\color{#c00}3,$ to $,\color{#0a0}2\ \ $ – Bill Dubuque Mar 04 '21 at 19:20
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Hint:
Solve the initial congruence $\;3x\equiv -5\mod 16$. As $3$ is coprime to $16$, it is invertible $\bmod16$, and the inverse is deduced from a Bézout's relation $\;3u+16v=1$, which shows the inverse of $3\bmod 16$ is the congruence class of $u$.
Bernard
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