If (ax + b)(bx + a) = 26x^2 + v * x + 26, where a,b , and v are distinct integers, what is the minimum possible value of v, the coefficient of x?
(ax + b) ( bx + a) = ab x^2 + ( a^2 + b^2) x + ab
So..equating coefficients, then ab = 26 and a^2 + b^2 = v
If ab = 26 and a,b are distinct intergers....then we have the following possibilities for a,b
a b a^2 + b^2
26 1 26^2 + 1^2 = 677
13 2 13^2 + 2^2 = 173
So...the minimum value for v = 173