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3 solutions
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Yes only guessing can work but probability that your guess is correct at first attempt is 3 1 .
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It reduces to 2 options as we can see that the denominator divides 75 powers of 3 and so does the numerator so the answer can't be 0.
We get 3 attempts too!
Pls explain?
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64 i s congruent to 1 mod 3 it means when u divide 64 with 3 remainder is 1 so when 64 is raised to any power it is also congruent to 1 mod 3
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But it is ( 1 5 8 − 6 4 ) ! 6 4 ! 1 5 8 ! = 9 4 ! 6 4 ! 1 5 8 ! .
There are only three possible values in m o d 3 : 0 , 1 , and 2 . Because you have three tries to get this right, you can just try all three, and you will be right for one of them (I know, I know, it's cheating)
what is lucas theorem can u explain it
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You can check wiki which i wrote in number theory section.
Use python -_- . 2 seconds of code :# :3
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https://brilliant.org/wiki/lucas-theorem/?subtopic=modular-arithmetic&chapter=modular-arithmetic#lucas-theorem
"even you python'ed"
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Yes, But I can't believe that you did so @Kartik Sharma
64=1mod3 so when 64 is raised to any power it is 1 only