Number theory

Nice, Number Theory lets go harder.

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NUMBER THEORY PROBLEM (Challenging)

Find all integers such that:

x^2 – 5x + 6 equiv 0 pmod{7}

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Solution

We solve this using Modular Arithmetic.

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Step 1: Work modulo 7

We test values of from to (since modulo 7 repeats).

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Step 2: Try values

Substitute into:

x^2 – 5x + 6 pmod{7}

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Step 3: Solutions modulo 7

x equiv 2 pmod{7}, quad x equiv 3 pmod{7}

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Final Answer

All integers of the form:

x = 7k + 2 quad text{or} quad x = 7k + 3

where is any integer

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