Question

remainder of 7^103 when divided by 17
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Answer 1

Answer:

the answer is 7

Step-by-step explanation:

7 * 103= 721

17*42= 714

721-714= 7

Answer 2

Given:

7^103 when divided by 17

Find:

The remainder of 7^103 when divided by 17.

Solution:

$7 * 103= 721\\17*42= 714721-714= 7$

Answer 3

Answer:

The remainder when $7^{103}$ is divided by $17$ is $12$

Step-by-step explanation:

Given:

To find the remainder when $7^{103}$ is divided by $17$

Since $GCD(7, 17)=1$, we can apply FLT, that is Fermat’s Little Theorem

$7^{17-1}=1$(Mod $17$)

$7^{103}=7^{(16*6+7)}=(1^6)*(7^7)$ (mod $17$)

$7^{-2}=-2$(mod $17$)

$7^7=(-2)^3*7=(-8)(-10)=12$(mod $17$)

Hence the remainder is $12$