- #1
songoku
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Homework Statement
Let n be an odd integer ≥ 5. Find the number of triplets (x, y, z) of positive integers which satisfy the equation
x + y + 2z = n
Homework Equations
Do not know
The Attempt at a Solution
Let n = 2k + 1, k ≥ 2
x + y + 2z = n
2z = 2k + 1 - (x + y) ≤ 2k + 1 - 2 (because x + y ≥ 2)
2z ≤ 2k - 1
Then stuck
The answer is (n - 1)(n - 3)/4
Thanks