Is it true that, for every integer t≥ 1, there is some integer a such that binomnk=a (with 1≤ k≤ n/2) has exactly t solutions?

Erdős Problem #849 — Is it true that, for every integer $t\geq 1$ , there is some integer $a$ such that $\binom{n}{k}=a$ (with $1\leq k\leq n/2$ ) has exactly $t$ solutions?

At least 29 years old · documented by 1996

Is it true that, for every integer $t\geq 1$ , there is some integer $a$ such that $\binom{n}{k}=a$ (with $1\leq k\leq n/2$ ) has exactly $t$ solutions?

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.

binomial-coefficients number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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