Finding Values of k for 6k2+4k in the Form 6ab+5a+b?

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The discussion centers on determining values of k for which the expression 6k² + 4k can be represented in the form 6ab + 5a + b. Participants provide examples, such as k=1 yielding 10, which can be expressed as 6(0)(2) + 5(2) + 0. A key point raised is that while a must be a positive integer, b can be zero or greater. The conclusion is that for any rational k, one can always find corresponding integer values for a and b that satisfy the equation.

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can somebody please tell me if there is any way to find all values of k for which 6k2+4k is of form 6ab+5a+b? eg. for k=1, 6k2+4k=10=6x0x2+5x2+0
 
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I might have misunderstood the question, but Based on what you made a=2 and b=0. Can you give them any value you want?
In that case can't you always make a=0, b= (6K 2 +4k)?
So that 6k2+4k is always of the form 6ab+5a+b, where K is any rational number.
eg. for k=1, 6k2+4k=10=6x0x10+5x0+10
Or should I just go back to my lunch:wink:
 
yeah sorry about that, but a can't be 0. has to be a integer>0. b,though can be >=0
 

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