Prove-that-7-n-1-divide-3-7-n-5-7-n-1-for-any-positive-integers-n-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 157967 by HongKing last updated on 30/Oct/21

Prove that 7^(n+1) divide 3^7^n + 5^7^n - 1 for any positive integers n

$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{7}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\:\mathrm{divide}\:\:\mathrm{3}^{\mathrm{7}^{\boldsymbol{\mathrm{n}}} } \:+\:\mathrm{5}^{\mathrm{7}^{\boldsymbol{\mathrm{n}}} } \:-\:\mathrm{1} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integers}\:\:\boldsymbol{\mathrm{n}} \\ $$

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