Let the number (22) 2022 + (2022) leave the remainder a when divided by 3 and 
when divided by 7. Then 
is equal to
Text Solution
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Given that a be the remainder when (22) 2022 + (2022) 22 is divided by 3 and 
be the remainder when the same is divided by 7.
(22) 2022 + (2022) 22 = (21 + 1) 2022 + (2022) 22 .
Here (2022) 22 is divisible by 3 as 2022 is divisible by 3.
So on expanding (21 + i) 2022 , we get
(21 + 1) 2022 = 2022 C 0 (21) 2022 + 2022 C 1 (21) 2021 + ......+ 2022 C 2022 2022
= 3(3 2021 x 7 2022 + 2022 C l x 3 2020 x 7 2021 +......)+1
= 3k 1 + 1
In this case the remainder is 1
Hence, 
= 1
Therefore, the required answer is 5.
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