A conjecture for breakfast, anyone?
Here’s something to go with your coffee and eggs in the morning.
Do you know the answer to this?
1) If you have 3 odd prime numbers, is it always true that there is at least one of the three that divides the product of the other two leaving remainder one. ( Let p,q,r be three distinct odd primes. Is it true that at least one of these cases happens? qr = 1 mod p, pq = 1 mod r or pr = 1 mod q.)
I think it’s true, but can’t prove it.
er…if we consider 5,7,11
then
5.7 = 2 mod 11
5.11 = 6 mod 7
7.11 = 2 mod 5
Is that a counter-example? Or did I miss something?
Comment by marcus — October 1, 2005 @ 1:33 pm
hehe…that’s right. It is a counter example, seems I didn’t really bother looking hard enough…*blush*
Comment by uliang — October 1, 2005 @ 2:56 pm