Let p be a prime. Let S be a set of (p-1) integers, none of which are divisible by p. Show that some subset of S has a sum that has a remainder of 1 when divided by p.
(The sum of a set is defined as the sum of the elements of the set)
(In reply to
re: Yet another Erdos theorem by Richard)
"except that it is for products rather than sums."
Although I agree with everything you've proved, you still have not solved the problem at hand. A product that is 1 modulo p corresponds to a sum that is 0 modulo (p-1) when looking at the exponents. The problem at hand, however, deals with sums that are 1 modulo p, quite different from 0 modulo (p-1).
I will agree with you, however, that the cited Erdos paper does not have anything to do with this problem.
As a hint, I will tell you this: the solution I have in mind uses only the most elementary facts concerning prime numbers. No advanced mathematics like number theory or group theory are involved (though you are welcome to try to apply them if you would like).
re(2): Yet another Erdos theorem
