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seen Feb 22 '11 at 4:59

Feb
10
comment Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square
Is it enough to state that because each $y_i$ must be 0 or 1 and each $z_i$ must be even, that this uniquely specifies a and b? Or do I need to show that this will always be unique?
Feb
9
asked Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square
Feb
2
comment If $s$ and $g>0$ are integers, how can I prove that $x$ and $y$ exist satisfying $x+y=s$ and $(x,y)=g$ if and only if $g \mid s$?
Ah, that clears things up perfectly. Thank you.
Feb
2
comment If $s$ and $g>0$ are integers, how can I prove that $x$ and $y$ exist satisfying $x+y=s$ and $(x,y)=g$ if and only if $g \mid s$?
I'm very sorry, but I'm still having trouble wrapping my head around how this fits in. Does this eliminate the need to mention that g|0 and thus, the need to mention that g|(0x+sy)? If not, how do these follow one another?
Feb
2
comment If $s$ and $g>0$ are integers, how can I prove that $x$ and $y$ exist satisfying $x+y=s$ and $(x,y)=g$ if and only if $g \mid s$?
I'm not sure I understand what your hint is referring to. Can you offer a little more clarification please?
Feb
2
awarded  Student
Feb
2
asked If $s$ and $g>0$ are integers, how can I prove that $x$ and $y$ exist satisfying $x+y=s$ and $(x,y)=g$ if and only if $g \mid s$?