N-x32y-in-base-10-N-0-3-and-N-0-4-N-gt-8329-N-has-four-digits-Determinate-N-

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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