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For three consecutive odd integers to have the sum 123, the equation N + N+2 + N+4 = 123 must be solvable with N being an odd integer.

N + N+2 + N+4 = 123

3N + 6 = 123

3N = 117

N = 39

Since 39 is an odd integer, the solution is 39, 41, and 43.

If N were even, or if N resolved to a non-integer, then the problem would have been incorrectly stated and unsolvable.

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Q: What three consecutive odd integers have the sum of 123?
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