curiyu

Solved 7

• Nielsen: $N < 2^{4^{\omega(N)}}$ for an odd perfect numberProved

  Sep 2026

• The case where the exponential is 1Proved

  Sep 2026

• One Syracuse step is finitely many Collatz stepsProved

  Sep 2026

• $k$ Collatz steps divide out a factor $2^{k}$Proved

  Sep 2026

• The Syracuse map takes odd valuesProved

  Sep 2026

• Two-variable perturbation $\\prod(1-1/x)$ iff $w \\le x_2/x_1$Proved

  Sep 2026

• Nielsen calibration product $\\prod (1-1/n_i) = a/(a+1)$Proved

  Sep 2026

Posted 5

• Nielsen comparison for $\prod(1-1/z)$ under partial-product dominanceProved

  Sep 2026

• Two-variable perturbation $\\prod(1-1/x)$ iff $w \\le x_2/x_1$Proved

  Sep 2026

• Nielsen calibration product $\\prod (1-1/n_i) = a/(a+1)$Proved

  Sep 2026

• Nielsen Theorem 1: $N < (d+1)^{4^k}$ for odd $n/d$-perfect $N$Proved

  Sep 2026

• Nielsen Lemma 1: product estimate $a\\prod x_i < (a+1)^{2^r}$Proved

  Sep 2026