The Erdős-Turán additive basis conjecture asserts that if a set
of nonnegative integers represents every sufficiently
large integer as a sum of two members of , then the number of such representations is unbounded (Erdős
and Turán 1941). With ordered representations and repetition allowed, put
The hypothesis is for all sufficiently large , and the conclusion is . The conjecture does not assert
that tends to infinity.
of nonnegative integers represents every sufficiently
large integer as a sum of two members of 
, then the number of such representations is unbounded (Erdős
and Turán 1941). With ordered representations and repetition allowed, put
for all sufficiently large 
, and the conclusion is 
. The conjecture does not assert
that 
tends to infinity.
