Problems
No problem here has yet been reviewed by a person.
Let f_3(N) be the least size forcing a set A ⊆ 1,…,N to contain distinct a,b,c with a+b, a+c and b+c all in A. The upper bound f_3(N) ≤ 5N/8 + O(1) matches the standard construction [N/8,N/4] ∪ [N/2,N], so f_3(N) = 5N/8 + O(1).
Let p be a complex polynomial of degree n≥2 whose zeros all lie in the closed unit disk. For every zero a of p, there is a critical point ζ satisfying |ζ-a|<1, except when |a|=1 and p is a nonzero scalar multiple of z^n-a^n.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.