user6548
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 Mar20 awarded Popular Question Feb10 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? Feb9 asked Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square Feb2 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. Feb2 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? Feb2 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? Feb2 awarded Student Feb2 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 $g \mid s$?