Find the last two digits of 79^64
Question
Find the last two digits of 79^64
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Solution
To find the last two digits of 79^64, we can use the concept of cyclicity.
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First, we need to find the cycle of the last digit, which is 9. The cycle of 9 is 9, 1, 9, 1, 9, 1, ... which repeats every 2 numbers. So, 9^64 ends in 1.
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Next, we need to find the cycle of the tens digit, which is 7. The cycle of 7 is 7, 9, 3, 1, 7, 9, 3, 1, ... which repeats every 4 numbers. So, 7^64 ends in 1.
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Therefore, the last two digits of 79^64 are 11.
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