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Prime Quadruplets and Jump Conditions on Arithmetic Functions
We provide progress on the characterization of composite integers $n$ that satisfy the jump conditions $φ(n+12)=φ(n)+12$ and $σ(n+12)=σ(n)+12$ simultaneously. While it is known that prime quadruplets $(p,p+2,p+6,p+8)$ generate solutions $n=p(p+8)$, the complete characterization remains an open conje
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