Hello,
Can anyone please asssist with the following question:
Prove that a positive integer a > 1 is a square if and only if in the canonical form of a all the exponents of the primes are even integers.
I would surely appreciate it.
Simple, because "square" means there exists an integer such that,
.
Now, no matter what canonical prime decomposition has MUST have even prime exponents because of the square (it doubles everything). And then you have that must also have even exponents because of uniqueness of prime power decomposition.