Why do we use modulo properties

#1

why do we use modulus properties while solving questions. we can also do this by calculating power by math function and simply talking modulus.

#2

inorder to avoid integer overflow
modulo keeps the value in range
hence using the modulo properties is important
directly caculation a^b could result in a bigger value
a^ (b/2) mod m would reduce the number then again multiplying by a^(b/2) mod m would prevent any such overflow

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#3

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