Question

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

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

Answer 2

5^21 is the answer to the question.