math jj help

nz20000

21）n divided by 6 余 2, divided by 8 余 4, 问divided by 48 余几？ 20
【确认】20

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why?

arthur

例如20除6余2，除8余4，除48余20

Echo

不一定吧，那44除6余2，除8余4，除48余44
因该还有别的条件吧

isuffering

DISCUSSION:

SINCE
N=6A+2
N=8B+4

LET X,
N+X=6C
N+X=8D
N+X=24E

THEN
X=6C-6A-2=6(C-A-1)+4
X1=4,10,16,22,28,...

X=8D-8B-4=8(D-B-1)+4
X2=4,12,20,28,...

THEN
X=4, 28, ...
THAT IS
X=24F+4

THEN

N=(N+X)-X
  =24E-24F-4
  =24G+20

AND THEN
LET
G=2H
THEN
N=24G*2N+20
  =48H+20

LET
G=2H+1
THEN
N=24*(2H+1)+20
  =48N+44

THUS
IF N,
n divided by 6 余 2, divided by 8 余 4,
THEN
THE REMAIN OF N BE DIVIDED BY 48 CAN BE EITHER  20 OR 44.