Question : The remainder when $19^{19}+20$ is divided by 18, is:
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
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Correct Answer: 3
Solution : To find: The remainder when $19^{19}+20$ is divided by 18. Now, 19 $\equiv$ 1 (mod 18) ⇒ 1919 $\equiv$ 119 (mod 18) ⇒ 1919 $\equiv$ 1 (mod 18) ⇒ (1919 + 20) $\equiv$ (1 + 20) (mod 18) ⇒ (1919 + 20) $\equiv$ (1 + 2) (mod 18) (Since 20 divides by 18 leaves a remainder of 2) ⇒ (1919 + 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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Question : When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
Question : A number, when divided by 6, leaves a remainder of 3. When the square of the same number is divided by 6, the remainder is:
Option 1: 0
Option 4: 3
Question : When n is divided by 4, the remainder is 3. The remainder when 2n is divided by 4 is:
Option 1: 1
Option 3: 3
Option 4: 6
Question : When a number is divided by 45, the remainder is 21. What will be the remainder when the number is divided by 15?
Option 1: 6
Option 2: 5
Question : What will be the remainder when $7^{42}$ is divided by 48?
Option 1: 2
Option 2: 3
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