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In this study, we introduce new class of quaternion and octonion numbers associated with the Mersenne numbers. We define Mersenne quaternion and Mersenne-Lucas quaternion, Mersenne octonion and Mersenne-Lucas octonion by using the Mersenne numbers. We obtained generating functions and Binet formulas for the Mersenne and Mersenne-Lucas quaternion and octonion and some of interesting identities of these numbers.
2020 Mathematics Subject Classification: 11B83
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