Let N≥ 1. What is the largest t such that there are A_1,…,A_t⊆ 1,…,N with A_i cap A_j a non-empty arithmetic progression for all i≠ j?

Erdős Problem #272 — Let $N\geq 1$ . What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$ ?

About 45 years old · traced to 1981

Let $N\geq 1$ . What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$ ?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

additive-combinatorics arithmetic-progressions

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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