AMC 10 Daily Practice - Modular Arithmetic

Complete problem set with solutions and individual problem pages

Problem 1 Medium

Given that 7x\equiv 107\left( \text{mod}11 \right), the minimum value of \left| x \right| is            .

Answer:2

7x\equiv 107\left( \text{mod}11 \right),

7x\equiv 107-44\left( \text{mod}11 \right),

7x\equiv 63\left( \text{mod}11 \right),

x\equiv 9\left( \text{mod}11 \right),

∴x=-2, \left| x \right|=2.

Related Problems
Problem 2 AMC 10 Daily Practice - Modular Arithmetic
Problem 3 AMC 10 Daily Practice - Modular Arithmetic
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