Srishti97 wrote:

Sum of the products of integers as : ab+ac+ad+bc+bd+cd

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\((a+b+c+d)^2 = a^2+b^2+c^2+d^2 + 2(ab+ac+ad+bc+bd+cd)\)

\(ab+ac+ad+bc+bd+cd =\frac{(a+b+c+d)^2 - (a^2+b^2+c^2+d^2)}{2}\)

given \(a+b+c+d=4Q+3\)

\(a,b,c,d\) are positive integers, their minimum value is 1

When \((a^2+b^2+c^2+d^2)\) is maximum, then \(ab+ac+ad+bc+bd+cd\) will be minimum for a given \(a+b+c+d\).

\((a^2+b^2+c^2+d^2)\) will be maximum when \(a=1,b=1,c=1\) and \(d =4Q\)(any three of them can be 1 ,4th one have to be \(4Q\))

Minimum value of \(ab+ac+ad+bc+bd+cd =1+1+4Q+1+4Q+4Q = 12Q + 3\)

Is this correct?