Status
On this page
Status
Topics
Status
On this page
Status
Topics
Is it true that if has no solutions to
then
Source: erdosproblems.com/867
An accepted solution exists. The statement is false.
DISPROVED (LEAN). Freud's construction (1993, a note in the James Cook Mathematical Notes) gives, for , a set of integers up to with no member a sum of two or more consecutive members, so grows like and no bound holds; repeating it with rapidly growing parameters gives an infinite sequence with . The acceptance evidence is the refereed paper of Coppersmith and Phillips (SIAM J. Discrete Math. 9 (1996), 173--177), whose Theorem 2.1 builds on Freud's construction (its reference [1]) and gives a set of such integers up to , a disproof in its own right, together with the site's label and thread; an external Lean file behind the catalog's label proves the consecutive-sum-freeness and the count of Freud's set for its own encoding; the corpus holds no build of it, so it gives no formalized evidence. The best bounds the site records are (Coppersmith and Phillips, Theorems 2.1 and 3.7; the printed upper bound is ); Freud's note reports their upper bound as , a figure the published paper does not print, recorded below. The standing is derived from the claim pages of Freud and Coppersmith and Phillips, both accepted on the evidence above.