Exercise · ZW-LINEAR-CONGRUENCE-008 · ★★☆ Intermediate

Solve \(2x \equiv 4 \pmod{6}\). How many solutions modulo 6 does it have?

Choose one option.

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  • D. 2

Explanation

Since \(\gcd(2,6)=2\) divides 4, the congruence has d=2 solutions modulo 6. Assuming a single solution is a common mistake.

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Review the concept: Linear congruence

A linear congruence is a first-degree congruence in one unknown \(x\), with integer coefficients \(a\), \(b\) and modulus \(m\); its solutions are the integers \(x\) that satisfy it.

\[ax \equiv b \pmod{m}\]

More practice problems: linear congruence

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