In this paper, we prove that for d = 3, 8, every natural number can be written as tx+ty +3tz +dtw, where x, y, z, and w are nonnegative integers and tk = k(k+1)/2 (k = 0, 1, 2,) is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.
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