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The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
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10 Answers

10 votes
10 votes
Alternatively,

$13*(13^{2})^{49}(mod \space 17) = 13*169^{49} (mod \space 16) = 13 * (-1)^{49} (mod\space 17) = -13 (mod\space 17) = 4$
7 votes
7 votes

I'm using Extended euclidean algorithm , Ans => 4

Algorithm =>

Computing answer =>

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0 votes

Like we find the unit place ( which follows the pattern ), here also it will follow the similar kinda pattern.

$13^{n}mod17$ will result in (1,13,16 or 4)

we needa check n mod 4

if n mod 4 = 0, result → 1

if n mod 4 = 1, result → 13

if n mod 4 = 2, result → 16

if n mod 4 = 3, result → 4

Answer to question 👇

$13^{99}mod17$ = 4 (bcoz 99 mod 4 = 3)

Answer:

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