Question

show that any positive integer can be written in the form of 3q, 3q+1, 3q+2, where q is some integer. answer too

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$let \: a \: be \: any \: positive \: integer \\ and \: b = 3 \\ so \: r = 0 \: or \: 1 \: or \: 2 \\ now \: by \: using \: euclids \: division \\ algorithm \: a = bq + r \: \\ we \: get \\ a = 3q + 0 = 3q \\ a = 3q + 1 \\ a = 3q + 2 \\ now \\ since \: all \: the \: three \: cases \: carry \\ the \: positive \: number \: as \: result \\ hence \\ we \: can \: say \: that \: any \: positive \\ integer \: is \: of \: the \: form \: \\ 3q \\ 3q + 1 \\ 3q + 2 \\ for \: some \: integer \: q.$
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