Question 1198925
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ANSWER: b) 5<br>
Look at the pattern of remainders when 4^n-1 is divided by 5:<br>
4^1-1 = 3; remainder when divided by 5 is 3
4^2-1 = 15; remainder when divided by 5 is 0
4^3-1 = 63; remainder when divided by 5 is 3
4^4-1 = 255; remainder when divided by 5 is 0<br>
The pattern repeats forever; the remainder when 4^1000-1 is divided by 5 is 0.<br>
You can find the similar patterns of remainders when 4^n-1 is divided by 7, 13, or 19; the length of the repeating patterns is such that 4^1000-1 will not be divisible by any of those other answer choices.<br>