Theory of numbers
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Quadratic Congruences. See attached file for full problem description.
Let p be an odd prime. Complete the proof of the question "For which odd primes p is LS(2, p) = 1?" by showing that if and that if .
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Solution Summary
The solution involves the problem of quadratic congruences.
Solution Preview
Please see the attached file.
If p is a prime number, then p-1, p-3, p+1, p+3 either of these is a multiple of 4. Also if p-1 is a multiple of 4, then p+3 is also multiple of 4. Similarly, if p-3 is a multiple of 4, so is the case of p+1
Solution:
We will prove this using the Gauss Lemma which is stated as follows
Let ...
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