Prove the divisibility of the following numbers: 5^23-5^21 by 24

Question

Mathematics

Arielle Cannon

12 July, 14:10

Prove the divisibility of the following numbers: 5^23-5^21 by 24

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Answers (1)

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Marlie Lutz · Answer 1

5^23 - 5^21 = 5^ (21+2) - 5^21

5^23 - 5^21 = 5^21*5^2 - 5^21*1

5^23 - 5^21 = 5^21 * (5^2 - 1)

5^23 - 5^21 = 5^21 * (25 - 1)

5^23 - 5^21 = 5^21*24

5^23 - 5^21 = 24*5^21

5^23 - 5^21 = 24*k

The original number is in the form 24k where k = 5^21, so this proves that the original number is a multiple of 24