How to find remainder using binomial theorem?
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Find the remainder when 7103 is divided by 24.
7103 is divided by 24.
Firstly, we know that 48 is divisible by 24 which can also be written as 49 is congruent to 1 mod 24. Thus, this can be simplified with the binomial expressions as
7103 = 7(50 - 1)51 = 7(5051 - 51C1 5050 + 51C2 5049 - ... - 1)
= 7(5051 - 51C15050 +...+ 51C5050) - 7 - 18 + 18
= 7(5051 - 51C15050 +...+ 51C5050) - 25 + 18
=> remainder is 18.
7103 is divided by 24.
Firstly, we know that 48 is divisible by 24 which can also be written as 49 is congruent to 1 mod 24. Thus, this can be simplified with the binomial expressions as
7103 = 7(50 - 1)51 = 7(5051 - 51C1 5050 + 51C2 5049 - ... - 1)
= 7(5051 - 51C15050 +...+ 51C5050) - 7 - 18 + 18
= 7(5051 - 51C15050 +...+ 51C5050) - 25 + 18
=> remainder is 18.
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