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Let b be an odd number. By using elementary methods, we prove that: (1) When x is an odd number and y is an even number, the Diophantine equation (2x−1)(by−1)=2z2… Click to show full abstract
Let b be an odd number. By using elementary methods, we prove that: (1) When x is an odd number and y is an even number, the Diophantine equation (2x−1)(by−1)=2z2 has no positive integer solution except when b is two special types of odd number. (2) When x is an odd number and b≡±3(mod8), the Diophantine equation (2x−1)(by−1)=2z2 has no positive integer solution except where b=3 and is another special type of the odd number.
Keywords:
diophantine equation;
number;
special type;
odd number;
equation 2z2
Journal Title: Mathematics
Year Published: 2023
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Journal Title: Mathematics
Year Published: 2023
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!