[數學]數論之Quadratic Residues 4個問題 (2008/05/11)

[數學]數論之Quadratic Residues 4個問題 (2008/05/11)

biology512 於 星期日 五月 11, 2008 3:15 pm


請證明以下4個問題
1.Let p be an odd prime number.Prove that the (p-1)/2 quadratic residues modulo p are congruent to 12 22 32 •••[(p-1)/2]2 Modulo p.
2
(a)Let p be a prime number with p>3.Prove that the sum of the quadratic residues modulo p is divisible by p.
(b)Let p be a prime number with p>5.Prove that the sum of the squares of the quadratic residues modulo p is divisible by p.
3.Let p be an odd prime number.Prove that the product of the quadratic residues modulo p is congruent to 1 modulo p if and only if p and 3 mod 4

以上問題採自 Elementary Number Theory,Strayer,Chapter 4-1 exercise 6,7,8

biology512
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註冊時間: 2008-05-11






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