Problem C: Pseudoprime numbers
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 by
p, 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 contains several test cases followed by a line containing "0 0". Each
test case consists of a line containing p and a. 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
Output for Sample Input
no
no
yes
no
yes
yes
Gordon V. Cormack