1 O ct 2 00 8 A NOTE ON SIERPIŃSKI PROBLEM RELATED TO TRIANGULAR NUMBERS
نویسنده
چکیده
In this note we show that the system of equations tx + ty = tp, ty + tz = tq , tx + tz = tr , where tx = x(x + 1)/2 is a triangular number, has infinitely many solutions in integers. Moreover we show that this system has rational three-parametric solution. Using this result we show that the system tx + ty = tp, ty + tz = tq , tx + tz = tr , tx + ty + tz = ts has infinitely many rational two-parametric solutions.
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