a positive integer n is divided by 9 leave the reminder 7 what will be the reminder when 3n-1 is divided by 9
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As n is the integer therefore n=9q+7
Now multiplying 3 on both sides we get,
3n = 27q+21
Now subtracting 1 from both sides we get
3n-1=27q+21-1
=>3n-1=27q+20
=>3n-1=27q+18+2
=>3n-1=9(3q+2) +2
=>3n-1=9m+2
Therfore the remainder is 2
Now multiplying 3 on both sides we get,
3n = 27q+21
Now subtracting 1 from both sides we get
3n-1=27q+21-1
=>3n-1=27q+20
=>3n-1=27q+18+2
=>3n-1=9(3q+2) +2
=>3n-1=9m+2
Therfore the remainder is 2
mayank223:
thank you for clarifying my doubts
Welcome . glad it helped.
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