How to find the integer values?Let N = 3 k − 8 k + 4 where k is an integer.List all positive values of k for which N is an integer.Do this using algebra, without using a calculator.Also do not do this by enumeration, i.e., plugging in k = 1 , 2 , . . . and checking the value of N.

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How to find the integer values?Let   N  =            3      k      −      8              k      +      4      where k is an integer.List all positive values of k for which N is an integer.Do this using algebra, without using a calculator.Also do not do this by enumeration, i.e., plugging in   k  =  1  ,  2  ,  .  .  . and checking the value of N.

Emma Cooper · Accepted Answer

The hint:            3      k      −      8              k      +      4        =            3      k      +      12      −      20              k      +      4        =  3  −      20          k      +      4        ,which says that   20 is divisible by   k  +  4Id est,  k  +  4  ∈  {  5  ,  10  ,  20  }because   k  &amp;gt;  0

How to find the integer values? Let N = (3k−8)/(k+4) where k is an integer. List all positive values of k for which N is an integer. Do this using algebra, without using a calculator. Also do not do this by enumeration, i.e., plugging in k=1,2,... and checking the value of N.

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