Write down the first few powers of 2 and look for a pattern in their unit digits.

Can you solve it? How can a unit digit be divided by 9?

Can you check if the answer is 5?

You can check the answer above. I have blurred the answer, and yes it is 5. How do you do it?

2^{1} has remainder 2 when divided by 9.

2^{2} has remainder 4 when divided by 9.

2^{3} has remainder 8 when divided by 9.

2^{4} has remainder 7 when divided by 9.

2^{5} has remainder 5 when divided by 9.

2^{6} has remainder 1 when divided by 9.

2^{7} has remainder 2 when divided by 9.

2^{8} has remainder 4 when divided by 9.

And so on - do you see the pattern? It can be shown that the 5th, 11th, 17th and so on would have remainder 5. 89 is part of that sequence.

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Got ya! thanks