Is There a Name for This Theorem?

Dschumanji

Is there a theorem that says when b|a² → b|a is true for integers a and b?

If so, what is it called?

haruspex

I hope not, since it isn't generally true. 9|36, but not 9|6. You would need that b is a prime (or at least, has no repeated prime factors).

daniel.e2718

OP, did you mean to reverse those...?

[itex]b|a \; \rightarrow \; b|a^{2}[/itex]

Is certainly true.

AlephZero

Quote by daniel.e2718

Is certainly true.

But it's hardly worth calling it a theorem, since it's just a special case of ##b|a \rightarrow b|ac##.

Benn

Quote by Dschumanji

Is there a theorem that says when b|a² → b|a is true for integers a and b?

If so, what is it called?

Millennial

The statement holds true whenever [itex]|\mu(b)|=1[/itex].

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Dschumanji	Is There a Name for This Theorem? Tweet Is there a theorem that says when b\|a² → b\|a is true for integers a and b? If so, what is it called?

haruspex Recognitions: Homework Help Science Advisor	I hope not, since it isn't generally true. 9\|36, but not 9\|6. You would need that b is a prime (or at least, has no repeated prime factors).

daniel.e2718	OP, did you mean to reverse those...? [itex]b\|a \; \rightarrow \; b\|a^{2}[/itex] Is certainly true.

Millennial	The statement holds true whenever [itex]\|\mu(b)\|=1[/itex].