/sci/ - Science & Math

>>14862389
It is not.
So the lemma you want is:
>Let a and b be positive integers, and suppose a^2 divides b^2. Then a divides b.
The proof is by looking at the exponents of the prime factors in the prime factorization of a^2 and b^2. Hint: the difference of two even numbers is also an even number. Use this to prove that the exponent of each prime factor in c = b^2 / a^2 is even, hence c is a square number.
Now you can use a^2 | a^3 and transitivity of the binary divides relation to demonstrate a^3|b^2=>a|b.
https://archive.org/details/introductiontoth0000nive