Two In One

Algebra Level 4

(1+3+5++pth)+(1+3+5++qth)=(1+3+5++rth) \left (1 + 3 + 5 + \ldots + p^\text{th} \right ) \\ + \\ \left (1 + 3 + 5 + \ldots + q^\text{th} \right ) \\ = \\ \left (1 + 3 + 5 + \ldots + r^\text{th} \right )

Given the above equation for positive integers p,q,rp,q,r with pthp^\text{th} term greater than 39.

What is the smallest possible value of the expression below?

pth term +qth term +rth term  \large p^\text{th} \ \text{term } + q^\text{th} \ \text{term } + r^\text{th} \ \text{term }

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