N=x32y in base 10. N≡0[3] and N≡0[4]. N>8329 N has four digits. Determinate N.


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Question Number 125672 by mathocean1 last updated on 12/Dec/20

$N = x 32 y i n b a s e 10 .$ $N \equiv 0 [3] a n d N \equiv 0 [4] .$ $N > 8329$ $N h a s f o u r d i g i t s .$ $D e t e r m i n a t e N .$
	Answered by JDamian last updated on 12/Dec/20

	$x + 3 + 2 + y \equiv 0 [3] \to x + y \equiv 1 [3]$ $N > 8329 \to x = 9 \to y \equiv 1 [3] \to y \in {1, 4, 7}$ $N \equiv 0 [4] \to 2 \times 2 + y \equiv 0 [4] \to y \equiv 0 [4]$ $y = 4$ $N = 9324$
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