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Author: Tinku Tara

knowing-that-7-3k-1-7-mod-9-k-N-show-that-2005-2005-7-mod-9-

Question Number 127132 by mathocean1 last updated on 27/Dec/20 $${knowing}\:{that}\:\mathrm{7}^{\mathrm{3}{k}+\mathrm{1}} \equiv\mathrm{7}\left[{mod}\:\mathrm{9}\right]\:;{k}\:\in\:\mathbb{N}. \\ $$$${show}\:{that}\:\mathrm{2005}^{\mathrm{2005}} \equiv\mathrm{7}\left[{mod}\:\mathrm{9}\right] \\ $$ Answered by JDamian last updated on 27/Dec/20 $$\mathrm{2005}\equiv\mathrm{7}\:{mod}\:\mathrm{9} \\…