1527 - Pseudoprime numbers
Time Limit : 1 Second
Memory Limit : 128 MB
Submission: 14
Solved: 4
- Description
Fermat's theorem states that for any prime number p and for any integer a > 1, ap == a (mod p). That is, if we raise a to the pth power and divide byp, the remainder is a. Some (but not very many) non-prime values of p, known as base-a pseudoprimes, have this property for some a. (And some, known as Carmichael Numbers, are base-a pseudoprimes for all a.)
Given 2 < p ≤ 1,000,000,000 and 1 < a < p, determine whether or not p is a base-a pseudoprime.
- Input
- Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing p and a.
- Output
- For each test case, output "yes" if p is a base-a pseudoprime; otherwise output "no".
- sample input
-
3 2 10 3 341 2 341 3 1105 2 1105 3 0 0
- sample output
-
no no yes no yes yes
- hint
- source
- waterloo 23 September, 2007