Count(q) does not imply Count(p)

Søren Riis

July 1994


I solve a conjecture originally studied by M.Ajtai. It states that for different primes q,p the matching principles Count(q) and Count(p) are logically independent. I prove that this indeed is the case. Actually I show that Count(q) implies Count(p) exactly when each prime in p also is a factor in q.

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