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

Question

Mathematics

Braxton Huff

26 October, 01:32

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

+1

Answers (1)

Know the Answer?

Ernest Lee · 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