Find the remainder when 107^1444 is divided by 136
Answer (1)
1st Jul, 2019
hi suresh
is your question correct .i have tried thiswith a scietific calculator and its showing maths error .the question you have asked is quite interesting but like others i also don't know the exact method . you can use doubtnut or just ask your teacher for it .please comment below if you know how to solve it
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Comments (2)
We can split the denominator into two Co-prime numbers as 17 and 8.
First we'll find d remainder of 107^1444/17 ~5^1444/17=5^16n*5^4/17~~1*5^4/17
Remainder =13
So 107^1444 is a 17n+13 number
Next find the of 107^1444/8 in d same way
We will get 8n+1 number. This all can be done by using a remainder theorem.
Then the next step is to find a number below 136 that is divisible by both 17n+13 as well as 8n+1 number.
The list of 17n+13 numbers below 136 is:13,30,47,64,81,98,115 n 132.
81 can be seen to be an 8n+1 number too
Thus, the correct answer is 81
First we'll find d remainder of 107^1444/17 ~5^1444/17=5^16n*5^4/17~~1*5^4/17
Remainder =13
So 107^1444 is a 17n+13 number
Next find the of 107^1444/8 in d same way
We will get 8n+1 number. This all can be done by using a remainder theorem.
Then the next step is to find a number below 136 that is divisible by both 17n+13 as well as 8n+1 number.
The list of 17n+13 numbers below 136 is:13,30,47,64,81,98,115 n 132.
81 can be seen to be an 8n+1 number too
Thus, the correct answer is 81
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