สมการไดโอแฟนไทน์ 3^x+n^y=z^2 เมื่อ n≡2 (mod 3)
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บทคัดย่อ
ในงานวิจัยนี้ได้ศึกษาผลเฉลยทั้งหมดของสมการไดโอแฟนไทน์ เมื่อ
เป็นจำนวนเต็มที่ไม่เป็นลบ และ
เป็นจำนวนเต็มบวก โดยที่
โดยใช้ทฤษฎีบทของมิไฮเลสคูและทฤษฎีบทของหลูและหลี่ ผลการวิจัยพบว่า สมการไดโอแฟนไทน์ดังกล่าวมีผลเฉลยทั้งหมด ดังนี้
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