Question : The remainder when $19^{19}+20$ is divided by 18, is:
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 3
Solution :
To find: The remainder when $19^{19}+20$ is divided by 18.
Now, 19 $\equiv$ 1 (mod 18)
⇒ 19
19
$\equiv$ 1
19
(mod 18)
⇒ 19
19
$\equiv$ 1 (mod 18)
⇒ (19
19
+ 20) $\equiv$ (1 + 20) (mod 18)
⇒ (19
19
+ 20) $\equiv$ (1 + 2) (mod 18) (Since 20 divides by 18 leaves a remainder of 2)
⇒ (19
19
+ 20) $\equiv$ 3 (mod 18)
So, the remainder when $19^{19}+20$ is divided by 18 is 3.
Hence, the correct answer is 3.
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