Let F_k(N) be the largest size of a subset A⊆1,…,N containing no k distinct elements whose product is a square. For odd k≥5, is F_k(N)=(1-o(1))N?

Erdős Problem #121 — Avoiding an odd number of factors with square product

About 32 years old · traced to 1994

Let $F_k(N)$ be the largest size of a subset $A\subseteq\{1,\ldots,N\}$ containing no $k$ distinct elements whose product is a square. For odd $k\geq5$ , is $F_k(N)=(1-o(1))N$ ?

References

Primary source

T. Tao, On product representations of squares, arXiv:2405.11610 (2024).

Additional references

T. Tao, On product representations of squares, arXiv:2405.11610 (2024).

number-theory squares

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