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.
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 $\displaystyle c$ such that,
$\displaystyle c^2=a$.
Now, no matter what canonical prime decomposition $\displaystyle c$ has $\displaystyle c^2$ MUST have even prime exponents because of the square (it doubles everything). And then you have that $\displaystyle a$ must also have even exponents because of uniqueness of prime power decomposition.