Prove-or-disprove-that-minimum-value-of-n-which-satisfies-the-equation-10-n-1-mod-7-p-is-n-6-7-p-1-

Question Number 443 by prakash jain last updated on 04/Jan/15

Prove or disprove that minimum value

of n which satisfies the equation

10^{n} \equiv 1 (\mod 7^{p}) is n = 6 \times 7^{p - 1} .

Commented by 123456 last updated on 05/Jan/15

10^{n} = {k 7}^{p} + 1, k \in N

n = \log (7^{p} k + 1)

7^{p} k + 1 \overset{10}{\equiv} 0, k > 0 \lor k = 0

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