Conjunctive grammars over an alphabet ∑ = {a} are studied, with the focus on the special case with a unique nonterminal symbol. Such a grammar is equivalent to an equation X = φ(X) over sets of natural numbers, using union, intersection and addition. It is shown that every grammar with multiple nonterminals can be encoded into a grammar with a single nonterminal, with a slight modification of the language. Based on this construction, the compressed membership problem for one-nonterminal conjunctive grammars over {a} is proved to be EXPTIME-complete, while the equivalence, finiteness and emptiness problems for these grammars are shown to be undecidable.