Linear Diophantine Equation #3

Linear Diophantine Equations
  1. D - 2 = C
  2. E + C = D
  3. A + E = C

Hint

Answer

Adding up Equation 1 and Equation 2 results in:
D + E - 2 + C = C + D, which is equal to E - 2 = 0

Therefore, we can conclude that:
  • E = 2
In Equation 3, we can see that:
  • A + 2 = C
However, we also know that C + 2 = D, so we have an order of A < C < D, all increasing 2 in value. Given that the numbers are in a range of 1-5, the only possible solution is:
  • A = 1
  • C = 3
  • D = 5
We already know that E = 2, so the only remaining solution is that:
  • B = 4.
This solution works for all equations. So, the solution is:
  • A = 1
  • B = 4
  • C = 3
  • D = 5
  • E = 2