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Question

Express 11 as a linear combination of 1650 and 847.


Solution

1650 = 847 * 1 + 803
847 = 803 * 1 + 44
803 = 44 * 18 + 11
44 = 11 * 4 + 0
Now,
11 = 803 - (44*18)
  = 803 - (847 - 803)*18
  = 1650 - 847 - 18*847 + 803*18
 =  1650 - 19*847 + (1650 - 847)*18
  = 1650 - 19*847 + 18*1650 - 18*847
  = 19 * 1650 - 37 * 847

Hope you understand the query :)

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