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Prove-that-for-all-a-2-divisible-by-b-a-is-also-divisible-by-b-for-all-a-b-N-




Question Number 181039 by depressiveshrek last updated on 20/Nov/22
Prove that for all a^2  divisible by b,  a is also divisible by b  for all a, b ∈ N
$${Prove}\:{that}\:{for}\:{all}\:{a}^{\mathrm{2}} \:{divisible}\:{by}\:{b}, \\ $$$${a}\:{is}\:{also}\:{divisible}\:{by}\:{b} \\ $$$${for}\:{all}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$
Commented by mr W last updated on 20/Nov/22
it′s not true!  example:  4^2  is divisible by 8.  but 4 is not divisible by 8.
$${it}'{s}\:{not}\:{true}! \\ $$$${example}: \\ $$$$\mathrm{4}^{\mathrm{2}} \:{is}\:{divisible}\:{by}\:\mathrm{8}. \\ $$$${but}\:\mathrm{4}\:{is}\:{not}\:{divisible}\:{by}\:\mathrm{8}. \\ $$
Commented by depressiveshrek last updated on 20/Nov/22
what if a>b
$${what}\:{if}\:{a}>{b} \\ $$
Commented by Frix last updated on 20/Nov/22
what about a=21∧b=9
$$\mathrm{what}\:\mathrm{about}\:{a}=\mathrm{21}\wedge{b}=\mathrm{9} \\ $$

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