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Quadratic reciprocity notes

Hence for every prime p by the multiplicative

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Unformatted text preview: square mod p. Hence for every prime p, by the multiplicative property. 3. Let’s try to show 8911 is composite. Evaluate : At this point it is not hard to check that 11 is NOT a square mod 23, but we can continue: Unfortunately, 30014455%8911= , so this doesn’t show 8911 is composite, but we know there is some b which will show it is composite. If fact, let b = 2. Then 28910%8911=1, so the Fermat test doesn’t work, but 24455%8911=6364, so the Euler test tells us that 8911 is composite, even without evaluating a Jacobi symbol....
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