Numerical answer
Find the remainder when 7^45 is divided by 100.
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Answer: 7
The last two digits (remainder mod 100) of powers of 7 cycle with period 4: 7¹=07, 7²=49, 7³=43, 7⁴=01, then it repeats. Since 45 = 4×11 + 1, 7^45 mod 100 has the same remainder as 7¹ mod 100, which is 7.
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