Triangular Number Equation: a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1)

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The forum discussion focuses on the triangular number equation: a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1). A specific solution is provided with a = 3 and b = 7, demonstrating that both sides of the equation are equal to T(a*b). The conclusion drawn is that this equality holds for any integers a and b, confirming the relationship between triangular numbers and the equation presented.

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Find all a,b such that a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1)

example solution a = 3, b = 7
 
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I think this holds for any (a, b).
 
Correct, both sides are always equal to T(a*b).
 

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