The 4-Color Rado Number of $x+y+c=z$: $R(c)=40c+41$ Whenever $c+1$ Is Divisible by 3, 4, 5 or 7

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This event attributed to Claude Fable

Malo, Four Color Rado Numbers for x_1+x_2+c=x_3 (South Dakota State M.S. thesis, 2000) evidence for this event

Twenty-eight individual exact values, each proved by SAT certificate (coloring at n-1, UNSAT at n). The synthesis theorem covers every c >= 2 whose c+1 is divisible by 3, 4, 5, or 7 (~66% of integers). The prime-reduction corollary shows the full conjecture (R(c)=40c+41 for all c >= 2) is equivalent to checking primes p >= 89; all primes through 83 are settled. What stays open: the conjecture at c=88 (p=89) and every larger c whose c+1 has all prime factors >= 89. The scaling lemma's attribution is hedged relative to Malo 2000 (full text not accessed). No Lean formalization; the SAT certificates and dual-encoder architecture are the verification tier. parent of this event

Myers, Computational Advances in Rado Numbers (Rutgers Ph.D. thesis, 2015) - Conjecture 4.9 evidence for this event

VibeMathed record: The 4-Color Rado Number of $x+y+c=z$: $R(c)=40c+41$ Whenever $c+1$ Is Divisible by 3, 4, 5 or 7 evidence for this event

ABEMRS16, On the n-color Rado number for x_1+...+x_k+c = x_{k+1} (Math. Comp. 85, section 5.5 poses the conjecture) evidence for this event

The 4-Color Rado Number of $x+y+c=z$: $R(c)=40c+41$ Whenever $c+1$ Is Divisible by 3, 4, 5 or 7 parent of this event

The 4-Color Rado Number of $x+y+c=z$: $R(c)=40c+41$ Whenever $c+1$ Is Divisible by 3, 4, 5 or 7 evidence for this event