52n-24n-1=125-24-1=100 is not divisible by 576.

When n = 2

52n-24n-1= 625-48-1= 576 is divisible by 576.

Suppose that when n = k

5 2k-24k- 1 is divisible by 576.

So when n = k+ 1

5^2(k+ 1)-24(k+ 1)- 1 = 5^2[5^2k-24k- 1]+5^2[24k+ 1]-24(k+ 1)- 1

= 5^2[5^2k-24k- 1]+(5^2- 1)5^2-24- 1

= 5^2[5^2k - 24k - 1] + 576k

So 5 2 (k+1)-24 (k+1)-1can also be divisible by 576.

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