Question 37

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

Solution

let's say k+4 = 7m
k = 7m-4
Now for k+2n or 7m+(2n-4) is also multiple of 7.
or 2n-4 should be a multiple of 7
So 2n-4 = 7p
or 2n = 7p+4
For p=2; n=9 (p cannot be 1 as n is an integer )

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Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

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