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mihisu
9 months ago

Your proof is wrong.

You claim and use that kgV(a., b.) = a.b. is. However, this does not apply in general, but only if a. and b. are part-nerd.

For example, on the one hand…

… and on the other hand…

kgV(4, 6) = 12 here not equal to 4 ⋅ 6 = 24.

===================

Here again about more formal with formula mode…

Destranix
9 months ago

That the statement is true is obvious. Because a cannot have a greater divider than a and kgV(a, b) definitely has a as a divider.

But I don’t think the proof is formal enough. You do not prove that T(a*b) and T(a) have exactly T(a) as a cut.

Of which: The smallest common multiple is not equivalent to the multiplication of the numbers.
See, for example, 12 and 18, multiple is 36.