2) V2 For every pair of distinct primes p and q, the rational 1/(pq) has the required one-term semiprime Egyptian-fraction representation.
kernel-checked, filed Tue Aug 25 2026 04:45:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Scope. An infinite family of positive squarefree-denominator rationals; the same dummy index, strict ordering, ω=Ω=2 condition, and rational sum convention as the root.
1) V1 Can every positive rational with squarefree reduced denominator be written as a finite sum of distinct unit fractions whose denominators are products of two distinct primes?
open, filed Tue Aug 25 2026 04:41:53 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The answer placeholder is resolved in the affirmative direction. `ω=Ω=2` is definitionally expanded in the differential gate and means precisely two distinct prime factors. The 2026 integer and threshold results do not cover every small positive rational with squarefree denominator.
Scope. All positive rationals q with squarefree reduced denominator; a dummy n(0)=1 precedes a strictly increasing finite list; every actual denominator has exactly two total and two distinct prime factors.