Can the expression $\alpha^{2κ-1}+\beta^{2κ-1}+\gamma^{2κ-1}\;$ be factorized

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enter image description hereenter image description here Is there an equation for the first picture, which fatorizes it in a similar fashion as the second pictures equation is factorized If so can you please tell me which equation it is and where I could find similar ones All the letters above are integers and ν in the second picture Is odd Thanking you in advance