What is the remainder when 8^24 is divided by 25?

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8 and 25 are coprime therefore 8^25-1 /25 = 1 ie 8^24/25=1

Answer will be 21 ...here 25 is not prime ..for fermats theorem to be applicable a and ap should be coprime and p should be prime

Answer is 21 and not 1.
8^24 = 64 ^12
64^12/25 = 14^12/25 = 196^6/25 =(-4)^6/25
=4^6/25
Since calculator is allowed , or simply 4^6 = 4096/25
Remainder is 21.
For that theorem to work 25 should have been prime.

21 IS CORRECT WRITE DOWN THE QSTN AS 2^72 NOW IT CAN BE WRITTEN AS 1024 MULTIPLIED 7TIMES*4 SO IT CAN BE WRITTEN AS (-1)^7*4 SO -4 IS THE REMAINDER OR 21 IS THE REMAINDER