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A:

If $n=1,21n+414n+3โ=21(1)+414(1)+3โ=21+414+3โ=2517โ$

is in the lowest form

If $n=2,21n+414n+3โ=21(2)+414(2)+3โ=42+428+3โ=4631โ$

is in the lowest form

Ifย

$n=3,21n+414n+3โ=21(3)+414(3)+3โ=63+442+3โ=6745โ$

is in the lowest form

ย Ifย

$n=4,21n+414n+3โ=21(4)+414(4)+3โ=84+456+3โ=88049โ$

is in the lowest form.

Similarly by substituting natural numbers for $n$ we can show that $21n+414n+3โ$ is in its lowest form.

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