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Find a recurrence relation for the number of bit sequences of length n with an odd number of 0s?



Find a recurrence relation for the number of bit sequences of length n with an odd number of 0s?



Prove: Use R - 3L for divisibility by 31.


Prove: Use R + 7L to determine if 23| N.


Prove: Methods for divisibility by 13.

  1. Method 2. ( R + 4L)Β 

Prove: 12|N iff 4| N ^ 3 | N.


Prove:

The following methods are useful for divisibility by 11.

  1. Get the difference of the sum of the digits in the odd places and the sum

of the digits in the even places. If the result is divisible by 11, then 11|N.


Prove that if π‘Ž|𝑏 and 𝑏≠0, then |π‘Ž| ≀ |𝑏|.


please find question on following link:


https://drive.google.com/file/d/1eEAAi25ydZMfBxtdiWMmwMoZSBuz643v/view?usp=sharing


please find question on following link:


https://drive.google.com/file/d/1eLr76-sYBNECsRB9GYNL0-aE3R5vHMpT/view?usp=sharing


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