GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 31

If x⁸⁶ ≡ 6 (mod 29), then value of x is/are ________ .
(A) 23
(B) 21
(C) 5
(D) None of these.

Answer: (B)
Explanation: Since 6 is relatively prime to 29, we have x⁸⁶ ≡ 6 (mod 29) implies x is relatively prime to 29.
So x²⁸ ≡ 1 (mod 29).
So since 86 ≡ 2 (mod 28), we have 6 ≡ ₂₉x⁸⁶ ≡ ₂₉x², which has solutions x = 8 and 21.

Option (B) is correct.
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