标题: 求解题-数论基础(英文题目，信息安全研究生)-~~英文好的进 [打印本页] 作者: eternityran 时间: 2011-10-17 08:23 标题: 求解题-数论基础(英文题目，信息安全研究生)-~~英文好的进 1. Verify that Φ(84)=Φ(12)Φ(7) by finding a bijection between ordered pairs.2 D( u* G9 H$ x& g
2. Programme Rowland's formular and verify his results. Try different starting values and see what happens. ( m3 b6 T9 T ]3. Verify the following result called Wilson's Theory: An integer n is prime if and only if (n-1)!≡-1(mod n ) for the cases n=2,3,4,5...,10. Can this be used as an efficent test for a prime? ' |9 g$ k9 ^5 u% H4. Prove that if n is a pseudoprime to base 2 then 2^n-1 is a pseudoprime to base 2 also.: w1 Q; [0 T! L1 g2 [
5. IS 341 a pseudoprime to the base 5? Is 341 a pseudoprime to base 7? Is 341 a pseudoprime to base 13? % m: l& `: ^/ T/ e* J6. Verify that 1729 and 2465 are Carmichael numbers using the Korselt criterion and directly. 7 n1 K {( f! A% C2 a8 z2 p1 k9 B7. Can pq be a Carmichael number where p and q are odd primes. 2 ~( K$ j: I2 J8. Find a k such that 6k+1,12k+1,18k+1 are all prime numbers. Prove that then n=(6k+1)(12k+1)(18k+1) is a Carmichael number. 0 _( O( H6 r, m- Z9 I* H9. Apply the Rabin-Miller test to n=1729 and n=2465& x- @8 E2 M- ?/ P6 B
10. Let n=667. For which a is a^667≡a(mod 667). Do the same for n=833. You might need to write a ** programme in Maple.