Joni Teräväinen

A conjecture of Erdős states that, for any large prime q , every reduced residue class ( mod ⁡ q ) {(\operatorname{mod}q)} can be represented as a product p 1 ⁢ p 2 {p_{1}p_{2}} of two primes p 1 , p 2 ≤ q {p_{1},p_{2}\leq q} . We establish a ternary version of this conjecture, showing that, for any sufficiently large cube-free integer q , every reduced residue class ( mod ⁡ q <m:mo