Triangular Numbers.....Part-2

Number Theory Level pending

Let \(t_{n}\) denote the \(n^{th}\) triangular number. Let \(t_{a},t_{b},t_{c}\) be three successive triangular numbers such that their sum is perfect square.Find the minimum possible value of \(a+b+c\).

Note- A triangular number is a number in the form of \(\frac{n(n+1)}{2}\) where \(n\ge1\).

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