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2 to the power of 2018 when divided by 17 what is the remainder
Asked by Girijeshpandey.rjil | 31 Mar, 2019, 09:53: AM
answered-by-expert Expert Answer
begin mathsize 12px style 2 to the power of 2018 space equals space open parentheses 2 to the power of 4 close parentheses to the power of 504 space 2 squared space equals space 4 open parentheses 17 minus 1 close parentheses to the power of 504 space equals space 4 space open square brackets 17 to the power of 504 space minus space C presuperscript 504 subscript 1 17 to the power of 503 space space space plus space C presuperscript 504 subscript 2 17 to the power of 502 space.......... negative C presuperscript 504 subscript 503 17 space plus space 1 to the power of 504 close square brackets end style .....................(1)
In the above eqn.(1), 17 can be factored out in all the terms of binomial expansion except the last term.
 
Hence eqn.(1) can be written as ,  22018 = 4 [ 17m + 1 ]  = (4×17×m)+4
where m is some integer
 
hence,  ( 22018 /17 ) = [ (4×17×m)+4 ] /17  ......................(2)
 
From eqn.(2), we get remainder 4
Answered by Thiyagarajan K | 31 Mar, 2019, 13:49: PM

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