if t_m +t_n and t_m −t_n is triangular number find the value of m+n


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Question Number 81007 by M±th+et£s last updated on 08/Feb/20

$i f t_{m} + t_{n} a n d t_{m} - t_{n} i s t r i a n g u l a r$ $n u m b e r f i n d t h e v a l u e o f m + n$
Commented by MJS last updated on 08/Feb/20

$this {doesn}^{'} t make much sense$ $if t_{j} is the j^{th} triangular number$ $t_{j} = \frac{j (j + 1)}{2}$ $\frac{m (m + 1)}{2} + \frac{n (n + 1)}{2} = \frac{m (m + 1)}{2} - \frac{n (n + 1)}{2}$ $\Rightarrow n = 0, m \in N \Rightarrow m + n = m$
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