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초록· 키워드
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In 1956, Je´smanowicz conjectured that, for any positive integer n and any primitive Pythagorean triple (a, b, c) with a2+b2 = c2, the equation (an)x+(bn)y = (cn)z has the unique solution (x, y, z) = (2, 2, 2).
In this paper, under some conditions, we prove the conjecture for the primitive Pythagorean triples (a, b, c) = (4k2 − 1, 4k, 4k2 + 1).
목차
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참고문헌 (16)
참고문헌 신청
De ´mjanenko / 1965 / On Je´smanowicz’ problem for Pythagorean numbers / Izv. Vyss. Ucebn. Zaved. Mat 48 (5) : 52 ~ 56
K. Takakuwa / 1993 / On a conjecture on Pythagorean numbers. II / Proc. Japan Acad. Ser. A Math. Sci 69 (8) : 287 ~ 290
K. Takakuwa / 1993 / On a conjecture on Pythagorean numbers. III / Proc. Japan Acad. Ser. A Math. Sci 69 (9) : 345 ~ 349
K. Takakuwa / 1996 / A remark on Je´smanowicz’ conjecture / Proc. Japan Acad. Ser. A Math. Sci 72 (6) : 109 ~ 110
L. Je´smanowicz / 1955 / Several remarks on Pythagorean numbers / Wiadom. Mat 1 : 196 ~ 202
K. Takakuwa / 1993 / On a conjecture on Pythagorean numbers. II / Proc. Japan Acad. Ser. A Math. Sci 69 (8) : 287 ~ 290
K. Takakuwa / 1993 / On a conjecture on Pythagorean numbers. III / Proc. Japan Acad. Ser. A Math. Sci 69 (9) : 345 ~ 349
K. Takakuwa / 1996 / A remark on Je´smanowicz’ conjecture / Proc. Japan Acad. Ser. A Math. Sci 72 (6) : 109 ~ 110
L. Je´smanowicz / 1955 / Several remarks on Pythagorean numbers / Wiadom. Mat 1 : 196 ~ 202
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