Conjectura Erdos Turan Modificata De Spanu Dumitru Viorel

Remark :

Conjectura Erdös – Turán modificată de Spânu Dumitru Viorel : “ If the sum of the reciprocals of a set of integers diverges , than that set contains infinitely long arithmetic progressions . “ The term infinitely long arithmetic progressions is better than arbitrarly long arithmetic progressions because , the aritmethic progressions contain an infinite number of terms . Of course , there are also arithmetic progressions of length k , if the sum of the reciprocals of a set of integers diverges , where k is a natural number , but then the arithmetic progressions are stopped forced . Only if the set is an infinite set , then the sum of the reciprocals of a set of integers diverges .

( Precizarea 4 pentru Conjectura modificata : Prin set intelegem notiunea de set infinit . ) For the rest of the conjecture , id est : “ For this first statement we will not take into consideration the sets constituted with the primes . For the next statement we will take into consideration the sets constituted with primes . If the sum of the reciprocals of a set of integers is either divergent or is convergent , than that set contains arbitrarily long arithmetic progressions . “ Precizarea 1 pentru Conjectura modificată : Din mulţimea numerelor intregi Z , vom exclude numărul zero . Precizarea 2 pentru Conjectura modificată : Conjectura Erdős-Turan modificată nu se referă la seriile alternante . Precizarea 3 pentru Conjectura modificata : Precizarea 2 nu se aplica seturilor formate din numere prime . Precizarea 4 pentru Conjectura modificata : Prin set intelegem notiunea de set infinit . “ I have no remark .