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

If x^{86} ≡ 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 x^{86} ≡ 6 (mod 29) implies x is relatively prime to 29.

So x^{28} ≡ 1 (mod 29).

So since 86 ≡ 2 (mod 28), we have 6 ≡ _{29}x^{86} ≡ _{29}x^{2}, which has solutions x = 8 and 21.

Option (B) is correct.

Quiz of this Question

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