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**[SOLVED] Proof Thery Exercise**

**1. Homework Statement**

Prove the following statement, where m and n are integers:

If x = 5m + 6 and y = 5n + 6, then xy = 5k + 6 for some integer k.

**2. Homework Equations**

**3. The Attempt at a Solution**

X = 5 m + 6, Y = 5 n + 6

X * Y = (5 m + 6) * (5 n + 6)

X * Y = (25 mn + 30 m + 30 n + 36)

5k + 6 = (25 mn + 30 m + 30 n + 36)

5k = (25 mn + 30 m + 30 n + 36) - 6

5k = (25 mn + 30 m + 30 n + 30)

k = (5mn + 6m + 6n + 6)

5k + 6 = 5 (5mn + 6m + 6n + 6) + 6

I am stuck, maybe its with another method like "Contradiction or Contrapositive" proof, any help will be appreciated.