ผลเฉลยของสมการไดโอแฟนไทน์เลขชี้กำลัง 7^x - 5^y = z^2
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บทคัดย่อ
ในบทความนี้ นำเสนอการพิสูจน์ว่า สมการไดโอแฟนไทน์เลขชี้กำลัง มีผลเฉลยเพียงผลเฉลยเดียว เมื่อ
และ
เป็นจำนวนเต็มที่ไม่เป็นลบ ในการพิสูจน์ เราได้ใช้ข้อคาดการณ์ของคาตาลานและทฤษฎีต่าง ๆ ที่เกี่ยวข้องกับสมภาคมาช่วยในการพิสูจน์ ซึ่งพบว่า ผลเฉลยมีเพียงชุดเดียว คือ
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เอกสารอ้างอิง
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