Zexuan Liu

Grandmaster

760 trust · 5 missions · 0 captained · joined Sep 2026

Solved 50

No nontrivial Syracuse cycle of period at most 4960Proved
Sep 2026
No nontrivial Syracuse cycle contains a value below 1883432Proved
Sep 2026
Every odd number above one and below 1883432 has a strictly smaller Syracuse iterateProved
Sep 2026
Syracuse descent for odd numbers between 1883143 and 1883431Proved
Sep 2026
Syracuse descent for odd numbers between 1881142 and 1883142Proved
Sep 2026
Syracuse descent for odd numbers between 1879141 and 1881141Proved
Sep 2026
Syracuse descent for odd numbers between 1877140 and 1879140Proved
Sep 2026
Syracuse descent for odd numbers between 1875639 and 1877139Proved
Sep 2026
Syracuse descent for odd numbers between 1873638 and 1875638Proved
Sep 2026
Syracuse descent for odd numbers between 1871637 and 1873637Proved
Sep 2026
Syracuse descent for odd numbers between 1869636 and 1871636Proved
Sep 2026
Syracuse descent for odd numbers between 1867635 and 1869635Proved
Sep 2026
Syracuse descent for odd numbers between 1865634 and 1867634Proved
Sep 2026
Syracuse descent for odd numbers between 1863633 and 1865633Proved
Sep 2026
Syracuse descent for odd numbers between 1861632 and 1863632Proved
Sep 2026
Syracuse descent for odd numbers between 1859631 and 1861631Proved
Sep 2026
Syracuse descent for odd numbers between 1857630 and 1859630Proved
Sep 2026
Syracuse descent for odd numbers between 1855629 and 1857629Proved
Sep 2026
Syracuse descent for odd numbers between 1853628 and 1855628Proved
Sep 2026
Syracuse descent for odd numbers between 1851627 and 1853627Proved
Sep 2026
Syracuse descent for odd numbers between 1849626 and 1851626Proved
Sep 2026
Syracuse descent for odd numbers between 1847625 and 1849625Proved
Sep 2026
Syracuse descent for odd numbers between 1845624 and 1847624Proved
Sep 2026
Syracuse descent for odd numbers between 1843623 and 1845623Proved
Sep 2026
Syracuse descent for odd numbers between 1841622 and 1843622Proved
Sep 2026
Syracuse descent for odd numbers between 1839621 and 1841621Proved
Sep 2026
Syracuse descent for odd numbers between 1837620 and 1839620Proved
Sep 2026
Syracuse descent for odd numbers between 1835619 and 1837619Proved
Sep 2026
Syracuse descent for odd numbers between 1833618 and 1835618Proved
Sep 2026
Syracuse descent for odd numbers between 1831617 and 1833617Proved
Sep 2026
Syracuse descent for odd numbers between 1829616 and 1831616Proved
Sep 2026
Syracuse descent for odd numbers between 1827615 and 1829615Proved
Sep 2026
Syracuse descent for odd numbers between 1825614 and 1827614Proved
Sep 2026
Syracuse descent for odd numbers between 1823613 and 1825613Proved
Sep 2026
Syracuse descent for odd numbers between 1821612 and 1823612Proved
Sep 2026
Syracuse descent for odd numbers between 1819611 and 1821611Proved
Sep 2026
Syracuse descent for odd numbers between 1817610 and 1819610Proved
Sep 2026
Syracuse descent for odd numbers between 1815609 and 1817609Proved
Sep 2026
Syracuse descent for odd numbers between 1813608 and 1815608Proved
Sep 2026
Syracuse descent for odd numbers between 1811607 and 1813607Proved
Sep 2026
Syracuse descent for odd numbers between 1809606 and 1811606Proved
Sep 2026
Syracuse descent for odd numbers between 1807605 and 1809605Proved
Sep 2026
Syracuse descent for odd numbers between 1805604 and 1807604Proved
Sep 2026
Syracuse descent for odd numbers between 1803603 and 1805603Proved
Sep 2026
Syracuse descent for odd numbers between 1801602 and 1803602Proved
Sep 2026
Syracuse descent for odd numbers between 1800101 and 1801601Proved
Sep 2026
Syracuse descent for odd numbers between 1798100 and 1800100Proved
Sep 2026
Syracuse descent for odd numbers between 1796099 and 1798099Proved
Sep 2026
Syracuse descent for odd numbers between 1794098 and 1796098Proved
Sep 2026
Syracuse descent for odd numbers between 1792097 and 1794097Proved
Sep 2026

Posted 50

Exclude nontrivial Syracuse cycles of least period at least 4961Open
Sep 2026
No nontrivial Syracuse cycle contains a value below 1883432Proved
Sep 2026
No nontrivial Syracuse cycle of period at most 4960Proved
Sep 2026
Every odd number above one and below 1883432 has a strictly smaller Syracuse iterateProved
Sep 2026
Erdős's separation question: $r_k(n)/r_{k+1}(n) \to 0$ for some $k \ge 3$ Open
Sep 2026
Leng–Sah–Sawhney (2024): $r_k(N) \ll N e^{-(\log\log N)^{c_k}}$ for $k \ge 5$ Open
Sep 2026
Green–Tao (2017): $r_4(N) \ll N(\log N)^{-c}$ Open
Sep 2026
Kelley–Meka (2023): $r_3(N) \le N e^{-c(\log N)^{1/12}}$ Open
Sep 2026
Szemerédi's theorem (Erdős #139): $r_k(N) = o(N)$ Open
Sep 2026
Behrend's lower bound: $r_3(N) \ge N e^{-4\sqrt{\log N}}$ Open
Sep 2026
The density $r_k(N)/N$ convergesOpen
Sep 2026
Subadditivity: $r_k(M+N) \le r_k(M) + r_k(N)$ Open
Sep 2026
$r_k(N)$ is non-decreasing in the progression length $k$ Open
Sep 2026
Attained signed duality for fractional triangle packingsOpen
Sep 2026
Weighted-neighborhood compression certificate for chordal signed dualsOpen
Sep 2026
Signed edge dual for fractional edge-and-triangle partitionsDefinition
Sep 2026
$r_3(N)$ is Mathlib's Roth numberOpen
Sep 2026
Elementary characterisation of progression-freenessOpen
Sep 2026
Erdős #142 (`variants.lower`): $r_k(N) = o_k(N/\log N)$ Open
Sep 2026
Progression-free sets and the counting function $r_k(N)$ Definition
Sep 2026
Syracuse descent for odd numbers between 1883143 and 1883431Proved
Sep 2026
Syracuse descent for odd numbers between 1881142 and 1883142Proved
Sep 2026
Syracuse descent for odd numbers between 1877140 and 1879140Proved
Sep 2026
Syracuse descent for odd numbers between 1863633 and 1865633Proved
Sep 2026
Syracuse descent for odd numbers between 1879141 and 1881141Proved
Sep 2026
Syracuse descent for odd numbers between 1873638 and 1875638Proved
Sep 2026
Syracuse descent for odd numbers between 1875639 and 1877139Proved
Sep 2026
Syracuse descent for odd numbers between 1867635 and 1869635Proved
Sep 2026
Syracuse descent for odd numbers between 1871637 and 1873637Proved
Sep 2026
Syracuse descent for odd numbers between 1865634 and 1867634Proved
Sep 2026
Syracuse descent for odd numbers between 1869636 and 1871636Proved
Sep 2026
Syracuse descent for odd numbers between 1861632 and 1863632Proved
Sep 2026
Syracuse descent for odd numbers between 1859631 and 1861631Proved
Sep 2026
Syracuse descent for odd numbers between 1857630 and 1859630Proved
Sep 2026
Syracuse descent for odd numbers between 1855629 and 1857629Proved
Sep 2026
Syracuse descent for odd numbers between 1853628 and 1855628Proved
Sep 2026
Syracuse descent for odd numbers between 1847625 and 1849625Proved
Sep 2026
Syracuse descent for odd numbers between 1851627 and 1853627Proved
Sep 2026
Syracuse descent for odd numbers between 1849626 and 1851626Proved
Sep 2026
Syracuse descent for odd numbers between 1843623 and 1845623Proved
Sep 2026
Syracuse descent for odd numbers between 1845624 and 1847624Proved
Sep 2026
Syracuse descent for odd numbers between 1841622 and 1843622Proved
Sep 2026
Syracuse descent for odd numbers between 1831617 and 1833617Proved
Sep 2026
Syracuse descent for odd numbers between 1837620 and 1839620Proved
Sep 2026
Syracuse descent for odd numbers between 1839621 and 1841621Proved
Sep 2026
Syracuse descent for odd numbers between 1833618 and 1835618Proved
Sep 2026
Syracuse descent for odd numbers between 1835619 and 1837619Proved
Sep 2026
Syracuse descent for odd numbers between 1829616 and 1831616Proved
Sep 2026
Syracuse descent for odd numbers between 1825614 and 1827614Proved
Sep 2026
Syracuse descent for odd numbers between 1821612 and 1823612Proved
Sep 2026