Numerical answer
Find the remainder when 7⁴⁵ is divided by 100.
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Answer: 7
The last two digits of powers of 7 cycle with period 4: 7¹=07, 7²=49, 7³=43, 7⁴=01, then it repeats (mod 100). Since 45 = 4×11 + 1, 7⁴⁵ ≡ 7⁴×¹¹ × 7¹ ≡ 1×7 ≡ 7 (mod 100). So the remainder is 7.
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