Each Natural Number Is of the Form X
نویسندگان
چکیده
In this paper we prove that any natural number n can be written as x + y + Tz with x, y, z ∈ Z and Tz = z(z + 1)/2. Also, we can express n in any of the following forms: x + y + 2Tz , x 2 + 2y + Tz , x 2 + 2y + 2Tz , x 2 + 2y + 4Tz , x + 2Ty + 2Tz , x 2 + 4Ty + Tz , x 2 + 4Ty + 2Tz , 2x + Ty + Tz , 2x 2 + 2Ty + Tz , 2x 2 + 4Ty + Tz , Tx + 4Ty + Tz , 2Tx + 2Ty + Tz , 2Tx + 4Ty + Tz . Concerning the converse we establish several theorems in the paper.
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تاریخ انتشار 2005